diff --git a/libs/utils/src/exp_counter.rs b/libs/utils/src/exp_counter.rs
index 89a59a9c45..161ac951cb 100644
--- a/libs/utils/src/exp_counter.rs
+++ b/libs/utils/src/exp_counter.rs
@@ -32,6 +32,12 @@ pub struct ExpCounter {
 }
 
 impl ExpCounter {
+    /// Creates an iterator that uses `ExpCounter` for the first half of the
+    /// range and a linear range counter for the second half.
+    pub fn with_max_and_linear_search(max: u64) -> impl Iterator<Item = u64> {
+        let linear_start = max / 2;
+        ExpCounter::with_max(linear_start).chain(linear_start..max)
+    }
     /// Creates a new `ExpCounter` instance that counts to the (exclusive) maximum
     pub fn with_max(max: u64) -> Self {
         Self {
diff --git a/pageserver/src/pgdatadir_mapping.rs b/pageserver/src/pgdatadir_mapping.rs
index 3b29f2d2cf..938672a908 100644
--- a/pageserver/src/pgdatadir_mapping.rs
+++ b/pageserver/src/pgdatadir_mapping.rs
@@ -370,7 +370,7 @@ impl Timeline {
             // We don't do an explosive search as we want to prove that
             // every single lsn up to high is giving inconclusive results.
             // This can only be done by trying all lsns.
-            for offs in ExpCounter::with_max(high - mid_start) {
+            for offs in ExpCounter::with_max_and_linear_search(high - mid_start) {
                 mid = offs + mid_start;
 
                 // Do the query for mid + 1 instead of mid so that we can make definite statements