diff --git a/Cargo.toml b/Cargo.toml
index d7864be30..72bdb6d34 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -50,6 +50,7 @@ murmurhash32 = "0.2"
 chrono = "0.4"
 smallvec = "1.0"
 rayon = "1"
+ordered-float = "1"
 
 [target.'cfg(windows)'.dependencies]
 winapi = "0.3"
@@ -58,6 +59,8 @@ winapi = "0.3"
 rand = "0.7"
 maplit = "1"
 matches = "0.1.8"
+proptest = "0.9"
+float-cmp = "0.6"
 
 [dev-dependencies.fail]
 version = "0.3"
diff --git a/src/postings/block_max_postings.rs b/src/postings/block_max_postings.rs
new file mode 100644
index 000000000..9ed93284c
--- /dev/null
+++ b/src/postings/block_max_postings.rs
@@ -0,0 +1,16 @@
+use crate::postings::Postings;
+use crate::DocId;
+
+/// Inverted list with additional information about the maximum term frequency
+/// within a block, as well as globally within the list.
+pub trait BlockMaxPostings: Postings {
+    /// Returns the maximum frequency in the entire list.
+    fn max_term_freq(&self) -> u32;
+    /// Returns the maximum frequency in the current block.
+    fn block_max_term_freq(&mut self) -> u32;
+    /// Returns the document with the largest frequency.
+    fn max_doc(&self) -> DocId;
+    /// Returns the document with the largest frequency within the current
+    /// block.
+    fn block_max_doc(&self) -> DocId;
+}
diff --git a/src/postings/block_max_segment_postings.rs b/src/postings/block_max_segment_postings.rs
new file mode 100644
index 000000000..58c8a8733
--- /dev/null
+++ b/src/postings/block_max_segment_postings.rs
@@ -0,0 +1,76 @@
+use crate::postings::{BlockMaxPostings, Postings, SegmentPostings};
+use crate::{DocId, DocSet, SkipResult};
+
+/// A wrapper over [`SegmentPostings`](./struct.SegmentPostings.html)
+/// with max block frequencies.
+pub struct BlockMaxSegmentPostings {
+    postings: SegmentPostings,
+    max_blocks: SegmentPostings,
+    doc_with_max_term_freq: DocId,
+    max_term_freq: u32,
+}
+
+impl BlockMaxSegmentPostings {
+    /// Constructs a new segment postings with block-max information.
+    pub fn new(
+        postings: SegmentPostings,
+        max_blocks: SegmentPostings,
+        doc_with_max_term_freq: DocId,
+        max_term_freq: u32,
+    ) -> Self {
+        Self {
+            postings,
+            max_blocks,
+            doc_with_max_term_freq,
+            max_term_freq,
+        }
+    }
+}
+
+impl DocSet for BlockMaxSegmentPostings {
+    fn advance(&mut self) -> bool {
+        self.postings.advance()
+    }
+
+    fn doc(&self) -> DocId {
+        self.postings.doc()
+    }
+
+    fn size_hint(&self) -> u32 {
+        self.postings.size_hint()
+    }
+
+    fn skip_next(&mut self, target: DocId) -> SkipResult {
+        self.postings.skip_next(target)
+    }
+}
+
+impl Postings for BlockMaxSegmentPostings {
+    fn term_freq(&self) -> u32 {
+        self.postings.term_freq()
+    }
+    fn positions_with_offset(&mut self, offset: u32, output: &mut Vec<u32>) {
+        self.postings.positions_with_offset(offset, output);
+    }
+    fn positions(&mut self, output: &mut Vec<u32>) {
+        self.postings.positions(output);
+    }
+}
+
+impl BlockMaxPostings for BlockMaxSegmentPostings {
+    fn max_term_freq(&self) -> u32 {
+        self.max_term_freq
+    }
+    fn block_max_term_freq(&mut self) -> u32 {
+        if matches!(self.max_blocks.skip_next(self.doc()), SkipResult::End) {
+            panic!("Max blocks corrupted: reached end of max block");
+        }
+        self.max_blocks.term_freq()
+    }
+    fn max_doc(&self) -> DocId {
+        self.doc_with_max_term_freq
+    }
+    fn block_max_doc(&self) -> DocId {
+        self.max_blocks.doc()
+    }
+}
diff --git a/src/postings/mod.rs b/src/postings/mod.rs
index b66beb413..aa25ae358 100644
--- a/src/postings/mod.rs
+++ b/src/postings/mod.rs
@@ -2,6 +2,8 @@
 Postings module (also called inverted index)
 */
 
+mod block_max_postings;
+mod block_max_segment_postings;
 mod block_search;
 pub(crate) mod compression;
 /// Postings module
@@ -29,6 +31,9 @@ pub use self::term_info::TermInfo;
 
 pub use self::segment_postings::{BlockSegmentPostings, SegmentPostings};
 
+pub use self::block_max_postings::BlockMaxPostings;
+pub use self::block_max_segment_postings::BlockMaxSegmentPostings;
+
 pub(crate) use self::stacker::compute_table_size;
 
 pub use crate::common::HasLen;
diff --git a/src/query/block_max_scorer.rs b/src/query/block_max_scorer.rs
new file mode 100644
index 000000000..3ece3adbf
--- /dev/null
+++ b/src/query/block_max_scorer.rs
@@ -0,0 +1,44 @@
+use crate::docset::DocSet;
+use crate::DocId;
+use crate::Score;
+use downcast_rs::impl_downcast;
+use std::ops::Deref;
+use std::ops::DerefMut;
+
+/// A set of documents matching a query within a specific segment
+/// and having a maximum score within certain blocks.
+///
+/// See [`Query`](./trait.Query.html) and [`Scorer`](./trait.Scorer.html).
+pub trait BlockMaxScorer: downcast_rs::Downcast + DocSet + 'static {
+    /// Returns the maximum score within the current block.
+    ///
+    /// The blocks are defined when indexing. For example, blocks can be
+    /// have a specific number postings each, or can be optimized for
+    /// retrieval speed. Read more in
+    /// [Faster BlockMax WAND with Variable-sized Blocks][vbmw]
+    ///
+    /// This method will perform a bit of computation and is not cached.
+    ///
+    /// [vbmw]: https://dl.acm.org/doi/abs/10.1145/3077136.3080780
+    fn block_max_score(&mut self) -> Score;
+
+    /// Returns the last document in the current block.
+    fn block_max_doc(&mut self) -> DocId;
+
+    /// Returns the maximum possible score within the entire document set.
+    fn max_score(&self) -> Score;
+}
+
+impl_downcast!(BlockMaxScorer);
+
+impl BlockMaxScorer for Box<dyn BlockMaxScorer> {
+    fn block_max_score(&mut self) -> Score {
+        self.deref_mut().block_max_score()
+    }
+    fn max_score(&self) -> Score {
+        self.deref().max_score()
+    }
+    fn block_max_doc(&mut self) -> DocId {
+        self.deref_mut().block_max_doc()
+    }
+}
diff --git a/src/query/block_max_wand.rs b/src/query/block_max_wand.rs
new file mode 100644
index 000000000..9e95d5a62
--- /dev/null
+++ b/src/query/block_max_wand.rs
@@ -0,0 +1,734 @@
+use crate::docset::{DocSet, SkipResult};
+use crate::query::score_combiner::ScoreCombiner;
+use crate::query::{BlockMaxScorer, Scorer};
+use crate::DocId;
+use crate::Score;
+
+#[derive(Debug, Copy, Clone, PartialEq, Eq)]
+struct Pivot {
+    position: usize,
+    first_occurrence: usize,
+    doc: DocId,
+}
+
+enum AdvanceResult {
+    Found,
+    Skipped,
+    End,
+}
+
+/// Find the position in the sorted list of posting lists of the **pivot**.
+fn find_pivot_position<'a, TScorer, F>(
+    mut docsets: impl Iterator<Item = &'a TScorer>,
+    condition: &F,
+) -> Option<Pivot>
+where
+    F: Fn(&Score) -> bool,
+    TScorer: BlockMaxScorer + Scorer,
+{
+    let mut position = 0;
+    let mut uppder_bound = Score::default();
+    while let Some(docset) = docsets.next() {
+        uppder_bound += docset.max_score();
+        if condition(&uppder_bound) {
+            let pivot_doc = docset.doc();
+            let first_occurrence = position;
+            while let Some(docset) = docsets.next() {
+                if docset.doc() != pivot_doc {
+                    break;
+                } else {
+                    position += 1;
+                }
+            }
+            return Some(Pivot {
+                position,
+                doc: pivot_doc,
+                first_occurrence,
+            });
+        }
+        position += 1;
+    }
+    None
+}
+
+/// Given an iterator over all ordered lists up to the pivot (inclusive) and the following list (if
+/// exists), it returns the next document ID that can be possibly relevant, based on the block max
+/// scores.
+fn find_next_relevant_doc<'a, T, TScorer>(
+    docsets_up_to_pivot: &'a mut [T],
+    pivot_docset: &'a mut T,
+    docset_after_pivot: Option<&'a mut T>,
+) -> DocId
+where
+    T: AsMut<TScorer>,
+    TScorer: BlockMaxScorer + Scorer,
+{
+    let pivot_docset = pivot_docset.as_mut();
+    let mut next_doc = 1 + docsets_up_to_pivot
+        .iter_mut()
+        .map(|docset| docset.as_mut().block_max_doc())
+        .chain(std::iter::once(pivot_docset.block_max_doc()))
+        .min()
+        .unwrap();
+    if let Some(docset) = docset_after_pivot {
+        let doc = docset.as_mut().doc();
+        if doc < next_doc {
+            next_doc = doc;
+        }
+    }
+    if next_doc <= pivot_docset.doc() {
+        pivot_docset.doc() + 1
+    } else {
+        next_doc
+    }
+}
+
+/// Sifts down the first element of the slice.
+fn sift_down<T, TScorer>(docsets: &mut [T])
+where
+    T: AsRef<TScorer>,
+    TScorer: BlockMaxScorer + Scorer,
+{
+    for idx in 1..docsets.len() {
+        if docsets[idx].as_ref().doc() < docsets[idx - 1].as_ref().doc() {
+            docsets.swap(idx, idx - 1);
+        } else {
+            break;
+        }
+    }
+}
+
+/// Creates a `DocSet` that iterates through the union of two or more `DocSet`s,
+/// applying [BlockMaxWand] dynamic pruning.
+///
+/// [BlockMaxWand]: https://dl.acm.org/doi/10.1145/2009916.2010048
+pub struct BlockMaxWand<TScorer, ThresholdFn, TScoreCombiner> {
+    docsets: Vec<Box<TScorer>>,
+    doc: DocId,
+    score: Score,
+    combiner: TScoreCombiner,
+    threshold_fn: ThresholdFn,
+}
+
+impl<TScorer, ThresholdFn, TScoreCombiner> BlockMaxWand<TScorer, ThresholdFn, TScoreCombiner>
+where
+    TScoreCombiner: ScoreCombiner,
+    TScorer: BlockMaxScorer + Scorer,
+    ThresholdFn: Fn(&Score) -> bool + 'static,
+{
+    fn new(
+        docsets: Vec<TScorer>,
+        combiner: TScoreCombiner,
+        threshold_fn: ThresholdFn,
+    ) -> BlockMaxWand<TScorer, ThresholdFn, TScoreCombiner> {
+        let mut non_empty_docsets: Vec<_> = docsets
+            .into_iter()
+            .flat_map(|mut docset| {
+                if docset.advance() {
+                    Some(Box::new(docset))
+                } else {
+                    None
+                }
+            })
+            .collect();
+        non_empty_docsets.sort_by_key(Box::<TScorer>::doc);
+        BlockMaxWand {
+            docsets: non_empty_docsets,
+            doc: 0,
+            score: 0f32,
+            combiner,
+            threshold_fn,
+        }
+    }
+
+    /// Find the position in the sorted list of posting lists of the **pivot**.
+    fn find_pivot_position(&self) -> Option<Pivot> {
+        find_pivot_position(
+            self.docsets.iter().map(|docset| docset.as_ref()),
+            &self.threshold_fn,
+        )
+    }
+
+    fn advance_with_pivot(&mut self, pivot: Pivot) -> AdvanceResult {
+        let block_upper_bound: Score = self.docsets[..=pivot.position]
+            .iter_mut()
+            .map(|docset| docset.block_max_score())
+            .sum();
+        if (self.threshold_fn)(&block_upper_bound) {
+            println!(
+                "Above T: {} ({:?})",
+                pivot.doc,
+                self.docsets.iter().map(|s| s.doc()).collect::<Vec<_>>()
+            );
+            if pivot.doc == self.docsets[0].doc() {
+                // NOTE(elshize): One additional check needs to be done to improve performance:
+                // update block-wise bound while accumulating score with the actual score,
+                // and check each time if still above threshold.
+                self.combiner.clear();
+                for idx in (0..=pivot.position).rev() {
+                    self.combiner.update(self.docsets[idx].as_mut());
+                    if !self.docsets[idx].advance() {
+                        self.docsets.swap_remove(idx);
+                    }
+                }
+                self.score = self.combiner.score();
+                self.doc = pivot.doc;
+                self.docsets.sort_by_key(Box::<TScorer>::doc);
+                AdvanceResult::Found
+            } else {
+                // The subraction is correct because otherwise we would go to the other branch.
+                let advanced_idx = pivot.first_occurrence - 1;
+                if !self.docsets[advanced_idx].advance() {
+                    self.docsets.swap_remove(advanced_idx);
+                }
+                if self.docsets.is_empty() {
+                    AdvanceResult::End
+                } else {
+                    sift_down(&mut self.docsets[advanced_idx..]);
+                    AdvanceResult::Skipped
+                }
+            }
+        } else {
+            let (up_to_pivot, pivot_and_rest) = self.docsets.split_at_mut(pivot.position as usize);
+            let (pivot, after_pivot) = pivot_and_rest.split_first_mut().unwrap();
+            let next_doc = find_next_relevant_doc(up_to_pivot, pivot, after_pivot.first_mut());
+            // NOTE(elshize): It might be more efficient to advance the list with the higher
+            // max score, but let's advance the first one for now for simplicity.
+            if self.docsets[0].skip_next(next_doc) == SkipResult::End {
+                self.docsets.swap_remove(0);
+            }
+            if self.docsets.is_empty() {
+                AdvanceResult::End
+            } else {
+                sift_down(&mut self.docsets[..]);
+                AdvanceResult::Skipped
+            }
+        }
+    }
+}
+
+impl<TScorer, ThresholdFn, TScoreCombiner> DocSet
+    for BlockMaxWand<TScorer, ThresholdFn, TScoreCombiner>
+where
+    TScorer: BlockMaxScorer + Scorer,
+    TScoreCombiner: ScoreCombiner,
+    ThresholdFn: Fn(&Score) -> bool + 'static,
+{
+    fn advance(&mut self) -> bool {
+        loop {
+            match {
+                if let Some(pivot) = self.find_pivot_position() {
+                    println!(
+                        "pivot = {:?}\n{:?}",
+                        pivot,
+                        self.docsets.iter().map(|s| s.doc()).collect::<Vec<_>>()
+                    );
+                    self.advance_with_pivot(pivot)
+                } else {
+                    println!(
+                        "[no pivot] {:?}",
+                        self.docsets.iter().map(|s| s.doc()).collect::<Vec<_>>()
+                    );
+                    AdvanceResult::End
+                }
+            } {
+                AdvanceResult::End => return false,
+                AdvanceResult::Found => return true,
+                _ => {}
+            }
+        }
+    }
+
+    fn skip_next(&mut self, target: DocId) -> SkipResult {
+        while self.doc() < target {
+            if !self.advance() {
+                return SkipResult::End;
+            }
+        }
+        if self.doc() == target {
+            SkipResult::Reached
+        } else {
+            SkipResult::OverStep
+        }
+    }
+
+    // TODO implement `count` efficiently.
+
+    fn doc(&self) -> DocId {
+        self.doc
+    }
+
+    fn size_hint(&self) -> u32 {
+        0u32
+    }
+
+    fn count_including_deleted(&mut self) -> u32 {
+        unimplemented!();
+    }
+}
+
+impl<TScorer, ThresholdFn, TScoreCombiner> Scorer
+    for BlockMaxWand<TScorer, ThresholdFn, TScoreCombiner>
+where
+    TScoreCombiner: ScoreCombiner,
+    TScorer: Scorer + BlockMaxScorer,
+    ThresholdFn: Fn(&Score) -> bool + 'static,
+{
+    fn score(&mut self) -> Score {
+        self.score
+    }
+}
+
+#[cfg(test)]
+mod tests {
+
+    use super::*;
+    use crate::common::HasLen;
+    use crate::docset::DocSet;
+    use crate::query::score_combiner::SumCombiner;
+    use crate::query::Union;
+    use crate::query::{BlockMaxScorer, Scorer};
+    use crate::{DocId, Score};
+    use float_cmp::approx_eq;
+    use ordered_float::OrderedFloat;
+    use proptest::strategy::Strategy;
+    use std::cmp::Ordering;
+    use std::collections::BinaryHeap;
+    use std::num::Wrapping;
+
+    #[derive(Debug, Clone)]
+    pub struct VecDocSet {
+        postings: Vec<(DocId, Score)>,
+        cursor: Wrapping<usize>,
+        block_max_scores: Vec<(DocId, Score)>,
+        max_score: Score,
+        block_size: usize,
+    }
+
+    impl VecDocSet {
+        fn new(postings: Vec<(DocId, Score)>, block_size: usize) -> VecDocSet {
+            let block_max_scores: Vec<_> = postings
+                .chunks(block_size)
+                .into_iter()
+                .map(|block| {
+                    (
+                        block.iter().last().unwrap().0,
+                        block
+                            .iter()
+                            .map(|(_, s)| OrderedFloat(*s))
+                            .max()
+                            .unwrap()
+                            .into_inner(),
+                    )
+                })
+                .collect();
+            let max_score = block_max_scores
+                .iter()
+                .copied()
+                .map(|(_, s)| OrderedFloat(s))
+                .max()
+                .unwrap();
+            VecDocSet {
+                postings,
+                cursor: Wrapping(0_usize) - Wrapping(1_usize),
+                block_max_scores,
+                max_score: max_score.into_inner(),
+                block_size,
+            }
+        }
+    }
+
+    impl DocSet for VecDocSet {
+        fn advance(&mut self) -> bool {
+            self.cursor += Wrapping(1);
+            self.postings.len() > self.cursor.0
+        }
+
+        fn doc(&self) -> DocId {
+            self.postings[self.cursor.0].0
+        }
+
+        fn size_hint(&self) -> u32 {
+            self.len() as u32
+        }
+    }
+
+    impl HasLen for VecDocSet {
+        fn len(&self) -> usize {
+            self.postings.len()
+        }
+    }
+
+    impl BlockMaxScorer for VecDocSet {
+        fn max_score(&self) -> Score {
+            self.max_score
+        }
+        fn block_max_score(&mut self) -> Score {
+            self.block_max_scores[self.cursor.0 / self.block_size].1
+        }
+        fn block_max_doc(&mut self) -> DocId {
+            self.block_max_scores[self.cursor.0 / self.block_size].0
+        }
+    }
+
+    impl Scorer for VecDocSet {
+        fn score(&mut self) -> Score {
+            self.postings[self.cursor.0].1
+        }
+    }
+
+    #[derive(Debug)]
+    struct ComparableDoc<T, D> {
+        feature: T,
+        doc: D,
+    }
+
+    impl<T: PartialOrd, D: PartialOrd> PartialOrd for ComparableDoc<T, D> {
+        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+            Some(self.cmp(other))
+        }
+    }
+
+    impl<T: PartialOrd, D: PartialOrd> Ord for ComparableDoc<T, D> {
+        #[inline]
+        fn cmp(&self, other: &Self) -> Ordering {
+            // Reversed to make BinaryHeap work as a min-heap
+            let by_feature = other
+                .feature
+                .partial_cmp(&self.feature)
+                .unwrap_or(Ordering::Equal);
+
+            let lazy_by_doc_address =
+                || self.doc.partial_cmp(&other.doc).unwrap_or(Ordering::Equal);
+
+            // In case of a tie on the feature, we sort by ascending
+            // `DocAddress` in order to ensure a stable sorting of the
+            // documents.
+            by_feature.then_with(lazy_by_doc_address)
+        }
+    }
+
+    impl<T: PartialOrd, D: PartialOrd> PartialEq for ComparableDoc<T, D> {
+        fn eq(&self, other: &Self) -> bool {
+            self.cmp(other) == Ordering::Equal
+        }
+    }
+
+    impl<T: PartialOrd, D: PartialOrd> Eq for ComparableDoc<T, D> {}
+
+    #[derive(Debug)]
+    struct TopSegmentCollector<T> {
+        limit: usize,
+        heap: BinaryHeap<ComparableDoc<T, DocId>>,
+    }
+
+    impl<T: PartialOrd> TopSegmentCollector<T> {
+        fn new(limit: usize) -> TopSegmentCollector<T> {
+            TopSegmentCollector {
+                limit,
+                heap: BinaryHeap::with_capacity(limit),
+            }
+        }
+    }
+
+    impl<T: PartialOrd + Clone + Copy + Default> TopSegmentCollector<T> {
+        pub fn harvest(self) -> Vec<(T, DocId)> {
+            self.heap
+                .into_sorted_vec()
+                .into_iter()
+                .map(|comparable_doc| (comparable_doc.feature, comparable_doc.doc))
+                .collect()
+        }
+
+        /// Return true iff at least K documents have gone through
+        /// the collector.
+        #[inline(always)]
+        pub(crate) fn at_capacity(&self) -> bool {
+            self.heap.len() >= self.limit
+        }
+
+        #[inline(always)]
+        pub(crate) fn above_threshold(&self, elem: &T) -> bool {
+            if self.at_capacity() {
+                elem > &self.heap.peek().unwrap().feature
+            } else {
+                true
+            }
+        }
+
+        /// Collects a document scored by the given feature
+        ///
+        /// It collects documents until it has reached the max capacity. Once it reaches capacity, it
+        /// will compare the lowest scoring item with the given one and keep whichever is greater.
+        #[inline(always)]
+        pub fn collect(&mut self, doc: DocId, feature: T) {
+            if self.at_capacity() {
+                // It's ok to unwrap as long as a limit of 0 is forbidden.
+                if let Some(limit_feature) = self.heap.peek().map(|head| head.feature.clone()) {
+                    if limit_feature < feature {
+                        if let Some(mut head) = self.heap.peek_mut() {
+                            head.feature = feature;
+                            head.doc = doc;
+                        }
+                    }
+                }
+            } else {
+                // we have not reached capacity yet, so we can just push the
+                // element.
+                self.heap.push(ComparableDoc { feature, doc });
+            }
+        }
+    }
+
+    fn union_vs_bmw(posting_lists: Vec<VecDocSet>) {
+        let mut union = Union::<VecDocSet, SumCombiner>::from(posting_lists.clone());
+        let mut top_union = TopSegmentCollector::<Score>::new(10);
+        while union.advance() {
+            top_union.collect(union.doc(), union.score());
+        }
+        let top_bmw = std::rc::Rc::new(std::cell::RefCell::new(TopSegmentCollector::<Score>::new(
+            10,
+        )));
+        let inner = std::rc::Rc::clone(&top_bmw);
+        let mut bmw = BlockMaxWand::new(posting_lists, SumCombiner::default(), move |score| {
+            let is_above = inner.borrow().above_threshold(score);
+            println!("{} (above = {})", score, is_above);
+            is_above
+        });
+        while bmw.advance() {
+            top_bmw.borrow_mut().collect(bmw.doc(), bmw.score());
+        }
+        drop(bmw);
+        for ((expected_score, expected_doc), (actual_score, actual_doc)) in
+            top_union.harvest().into_iter().zip(
+                std::rc::Rc::try_unwrap(top_bmw)
+                    .unwrap()
+                    .into_inner()
+                    .harvest(),
+            )
+        {
+            assert!(approx_eq!(
+                f32,
+                expected_score,
+                actual_score,
+                epsilon = 0.0001
+            ));
+            assert_eq!(expected_doc, actual_doc);
+        }
+    }
+
+    #[test]
+    fn test_bmw_0() {
+        union_vs_bmw(vec![
+            VecDocSet {
+                postings: vec![
+                    (0, 1.0),
+                    (23, 1.0),
+                    (28, 1.0),
+                    (56, 1.0),
+                    (59, 1.0),
+                    (66, 1.0),
+                    (93, 1.0),
+                ],
+                cursor: Wrapping(0_usize) - Wrapping(1_usize),
+                block_max_scores: vec![(93, 1.0)],
+                max_score: 1.0,
+                block_size: 16,
+            },
+            VecDocSet {
+                postings: vec![
+                    (2, 1.6549665),
+                    (43, 2.6958032),
+                    (53, 3.5309567),
+                    (71, 2.7688136),
+                    (87, 3.4279852),
+                    (96, 3.9028034),
+                ],
+                cursor: Wrapping(0_usize) - Wrapping(1_usize),
+                block_max_scores: vec![(96, 3.9028034)],
+                max_score: 3.9028034,
+                block_size: 16,
+            },
+        ])
+    }
+
+    #[test]
+    fn test_bmw_1() {
+        union_vs_bmw(vec![
+            VecDocSet {
+                postings: vec![(73, 1.0), (82, 1.0)],
+                cursor: Wrapping(0_usize) - Wrapping(1_usize),
+                block_max_scores: vec![(82, 1.0)],
+                max_score: 1.0,
+                block_size: 16,
+            },
+            VecDocSet {
+                postings: vec![
+                    (21, 3.582513),
+                    (23, 1.6928024),
+                    (27, 3.887647),
+                    (42, 1.5469292),
+                    (61, 1.7317574),
+                    (62, 1.2968783),
+                    (82, 2.4040694),
+                    (85, 3.1487892),
+                ],
+                cursor: Wrapping(0_usize) - Wrapping(1_usize),
+                block_max_scores: vec![(85, 3.887647)],
+                max_score: 3.887647,
+                block_size: 16,
+            },
+        ])
+    }
+
+    proptest::proptest! {
+        #[test]
+        fn test_union_vs_bmw(postings in proptest::collection::vec(
+            proptest::collection::vec(0_u32..100, 1..10)
+                .prop_flat_map(|v| {
+                    let scores = proptest::collection::vec(1_f32..4_f32, v.len()..=v.len());
+                    scores.prop_map(move |s| {
+                        let mut postings: Vec<_> = v.iter().copied().zip(s.iter().copied()).collect();
+                        postings.sort_by_key(|p| p.0);
+                        postings.dedup_by_key(|p| p.0);
+                        VecDocSet::new(postings, 16)
+                    })
+                }),
+            2..5)
+        ) {
+            union_vs_bmw(postings);
+        }
+    }
+
+    #[test]
+    fn test_find_pivot_position() {
+        let postings = vec![
+            VecDocSet::new(vec![(0, 2.0)], 1),
+            VecDocSet::new(vec![(1, 3.0)], 1),
+            VecDocSet::new(vec![(2, 4.0)], 1),
+            VecDocSet::new(vec![(3, 5.0)], 1),
+            VecDocSet::new(vec![(3, 6.0)], 1),
+        ];
+        assert_eq!(
+            find_pivot_position(postings.iter(), &|&score| score > 2.0),
+            Some(Pivot {
+                position: 1,
+                doc: 1,
+                first_occurrence: 1,
+            })
+        );
+        assert_eq!(
+            find_pivot_position(postings.iter(), &|&score| score > 5.0),
+            Some(Pivot {
+                position: 2,
+                doc: 2,
+                first_occurrence: 2,
+            })
+        );
+        assert_eq!(
+            find_pivot_position(postings.iter(), &|&score| score > 9.0),
+            Some(Pivot {
+                position: 4,
+                doc: 3,
+                first_occurrence: 3,
+            })
+        );
+        assert_eq!(
+            find_pivot_position(postings.iter(), &|&score| score > 20.0),
+            None
+        );
+    }
+
+    #[test]
+    fn test_find_next_relevant_doc_before_pivot() {
+        let mut postings = vec![
+            Box::new(VecDocSet::new(vec![(0, 0.0), (3, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(1, 0.0), (4, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(2, 0.0), (6, 0.0)], 2)), // pivot
+            Box::new(VecDocSet::new(vec![(6, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(6, 0.0), (8, 0.0)], 2)),
+        ];
+        let (up_to_pivot, rest) = postings.split_at_mut(2);
+        let (pivot, after_pivot) = rest.split_first_mut().unwrap();
+        let next_doc = find_next_relevant_doc(up_to_pivot, pivot, Some(&mut after_pivot[0]));
+        assert_eq!(next_doc, 4);
+    }
+
+    #[test]
+    fn test_find_next_relevant_doc_prefix_smaller_than_pivot() {
+        let mut postings = vec![
+            Box::new(VecDocSet::new(vec![(0, 0.0), (3, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(1, 0.0), (4, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(5, 0.0), (8, 0.0)], 2)), // pivot
+            Box::new(VecDocSet::new(vec![(6, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(6, 0.0), (8, 0.0)], 2)),
+        ];
+        let (up_to_pivot, rest) = postings.split_at_mut(2);
+        let (pivot, after_pivot) = rest.split_first_mut().unwrap();
+        let next_doc = find_next_relevant_doc(up_to_pivot, pivot, Some(&mut after_pivot[0]));
+        assert_eq!(next_doc, 6);
+    }
+
+    #[test]
+    fn test_find_next_relevant_doc_after_pivot() {
+        let mut postings = vec![
+            Box::new(VecDocSet::new(vec![(0, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(1, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(2, 0.0), (8, 0.0)], 2)), // pivot
+            Box::new(VecDocSet::new(vec![(5, 0.0), (7, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(6, 0.0), (7, 0.0)], 2)),
+        ];
+        let (up_to_pivot, rest) = postings.split_at_mut(2);
+        let (pivot, after_pivot) = rest.split_first_mut().unwrap();
+        let next_doc = find_next_relevant_doc(up_to_pivot, pivot, Some(&mut after_pivot[0]));
+        assert_eq!(next_doc, 5);
+    }
+
+    #[test]
+    fn test_sift_down_already_sifted() {
+        let mut postings = vec![
+            Box::new(VecDocSet::new(vec![(0, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(1, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(2, 0.0), (8, 0.0)], 2)), // pivot
+            Box::new(VecDocSet::new(vec![(5, 0.0), (7, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(6, 0.0), (7, 0.0)], 2)),
+        ];
+        sift_down(&mut postings[2..]);
+        assert_eq!(
+            postings.into_iter().map(|p| p.doc()).collect::<Vec<_>>(),
+            vec![0, 1, 2, 5, 6]
+        );
+    }
+
+    #[test]
+    fn test_sift_down_sift_one_down() {
+        let mut postings = vec![
+            Box::new(VecDocSet::new(vec![(0, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(1, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(6, 0.0), (8, 0.0)], 2)), // pivot
+            Box::new(VecDocSet::new(vec![(5, 0.0), (7, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(7, 0.0), (7, 0.0)], 2)),
+        ];
+        sift_down(&mut postings[2..]);
+        assert_eq!(
+            postings.into_iter().map(|p| p.doc()).collect::<Vec<_>>(),
+            vec![0, 1, 5, 6, 7]
+        );
+    }
+
+    #[test]
+    fn test_sift_down_to_bottom() {
+        let mut postings = vec![
+            Box::new(VecDocSet::new(vec![(0, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(1, 0.0), (8, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(7, 0.0), (8, 0.0)], 2)), // pivot
+            Box::new(VecDocSet::new(vec![(5, 0.0), (7, 0.0)], 2)),
+            Box::new(VecDocSet::new(vec![(6, 0.0), (7, 0.0)], 2)),
+        ];
+        sift_down(&mut postings[2..]);
+        assert_eq!(
+            postings.into_iter().map(|p| p.doc()).collect::<Vec<_>>(),
+            vec![0, 1, 5, 6, 7]
+        );
+    }
+}
diff --git a/src/query/mod.rs b/src/query/mod.rs
index 6f52784a5..5624aeffc 100644
--- a/src/query/mod.rs
+++ b/src/query/mod.rs
@@ -5,6 +5,8 @@ Query
 mod all_query;
 mod automaton_weight;
 mod bitset;
+mod block_max_scorer;
+mod block_max_wand;
 mod bm25;
 mod boolean_query;
 mod boost_query;
@@ -24,7 +26,6 @@ mod term_query;
 mod union;
 mod weight;
 
-
 #[cfg(test)]
 mod vec_docset;
 
@@ -38,13 +39,14 @@ pub use self::vec_docset::VecDocSet;
 pub use self::all_query::{AllQuery, AllScorer, AllWeight};
 pub use self::automaton_weight::AutomatonWeight;
 pub use self::bitset::BitSetDocSet;
+pub use self::block_max_scorer::BlockMaxScorer;
 pub use self::boolean_query::BooleanQuery;
 pub use self::boost_query::BoostQuery;
 pub use self::empty_query::{EmptyQuery, EmptyScorer, EmptyWeight};
 pub use self::exclude::Exclude;
 pub use self::explanation::Explanation;
-pub use self::fuzzy_query::FuzzyTermQuery;
 pub(crate) use self::fuzzy_query::DFAWrapper;
+pub use self::fuzzy_query::FuzzyTermQuery;
 pub use self::intersection::intersect_scorers;
 pub use self::phrase_query::PhraseQuery;
 pub use self::query::Query;
diff --git a/src/query/term_query/block_max_term_scorer.rs b/src/query/term_query/block_max_term_scorer.rs
new file mode 100644
index 000000000..33346ad00
--- /dev/null
+++ b/src/query/term_query/block_max_term_scorer.rs
@@ -0,0 +1,98 @@
+use crate::docset::{DocSet, SkipResult};
+use crate::query::{Explanation, Scorer};
+use crate::DocId;
+use crate::Score;
+
+use crate::fieldnorm::FieldNormReader;
+use crate::postings::Postings;
+use crate::postings::{BlockMaxPostings, BlockMaxSegmentPostings};
+use crate::query::bm25::BM25Weight;
+use crate::query::BlockMaxScorer;
+
+pub struct BlockMaxTermScorer {
+    postings: BlockMaxSegmentPostings,
+    fieldnorm_reader: FieldNormReader,
+    similarity_weight: BM25Weight,
+}
+
+impl BlockMaxTermScorer {
+    pub fn new(
+        postings: BlockMaxSegmentPostings,
+        fieldnorm_reader: FieldNormReader,
+        similarity_weight: BM25Weight,
+    ) -> Self {
+        Self {
+            postings,
+            fieldnorm_reader,
+            similarity_weight,
+        }
+    }
+}
+
+impl BlockMaxTermScorer {
+    fn _score(&self, fieldnorm_id: u8, term_freq: u32) -> Score {
+        self.similarity_weight.score(fieldnorm_id, term_freq)
+    }
+
+    pub fn term_freq(&self) -> u32 {
+        self.postings.term_freq()
+    }
+
+    pub fn fieldnorm_id(&self) -> u8 {
+        self.fieldnorm_reader.fieldnorm_id(self.doc())
+    }
+
+    pub fn explain(&self) -> Explanation {
+        let fieldnorm_id = self.fieldnorm_id();
+        let term_freq = self.term_freq();
+        self.similarity_weight.explain(fieldnorm_id, term_freq)
+    }
+}
+
+impl DocSet for BlockMaxTermScorer {
+    fn advance(&mut self) -> bool {
+        self.postings.advance()
+    }
+
+    fn skip_next(&mut self, target: DocId) -> SkipResult {
+        self.postings.skip_next(target)
+    }
+
+    fn doc(&self) -> DocId {
+        self.postings.doc()
+    }
+
+    fn size_hint(&self) -> u32 {
+        self.postings.size_hint()
+    }
+}
+
+impl Scorer for BlockMaxTermScorer {
+    fn score(&mut self) -> Score {
+        self._score(
+            self.fieldnorm_reader.fieldnorm_id(self.doc()),
+            self.postings.term_freq(),
+        )
+    }
+}
+
+impl BlockMaxScorer for BlockMaxTermScorer {
+    fn block_max_score(&mut self) -> Score {
+        self._score(
+            self.fieldnorm_reader
+                .fieldnorm_id(self.postings.block_max_doc()),
+            self.postings.term_freq(),
+        )
+    }
+
+    fn block_max_doc(&mut self) -> DocId {
+        self.postings.block_max_doc()
+    }
+
+    fn max_score(&self) -> Score {
+        self._score(
+            self.fieldnorm_reader.fieldnorm_id(self.postings.max_doc()),
+            self.postings.max_term_freq(),
+        )
+    }
+}
diff --git a/src/query/term_query/mod.rs b/src/query/term_query/mod.rs
index d38756b7e..8349bd6c4 100644
--- a/src/query/term_query/mod.rs
+++ b/src/query/term_query/mod.rs
@@ -1,7 +1,9 @@
+mod block_max_term_scorer;
 mod term_query;
 mod term_scorer;
 mod term_weight;
 
+pub use self::block_max_term_scorer::BlockMaxTermScorer;
 pub use self::term_query::TermQuery;
 pub use self::term_scorer::TermScorer;
 pub use self::term_weight::TermWeight;