diff --git a/test/boost/logalloc_test.cc b/test/boost/logalloc_test.cc
index 38a2dd54fc..d7240d9e1a 100644
--- a/test/boost/logalloc_test.cc
+++ b/test/boost/logalloc_test.cc
@@ -812,27 +812,20 @@ SEASTAR_THREAD_TEST_CASE(background_reclaim) {
         logalloc::shard_tracker().stop().get();
     });
 
-    sleep(500ms).get(); // sleep a little, to give the reclaimer a head start
-
     std::vector<managed_bytes> std_allocs;
     size_t std_alloc_size = 1000000; // note that managed_bytes fragments these, even in std
     for (int i = 0; i < 50; ++i) {
+        // Background reclaim is supposed to eventually ensure a certain amount of free memory.
+        while (memory::free_memory() < background_reclaim_free_memory_threshold) {
+            thread::maybe_yield();
+        }
+
         auto compacted_pre = logalloc::shard_tracker().statistics().memory_compacted;
         fmt::print("compacted {} items {} (pre)\n", compacted_pre, evictable_allocs.size());
         std_allocs.emplace_back(managed_bytes::initialized_later(), std_alloc_size);
         auto compacted_post = logalloc::shard_tracker().statistics().memory_compacted;
         fmt::print("compacted {} items {} (post)\n", compacted_post, evictable_allocs.size());
         BOOST_REQUIRE_EQUAL(compacted_pre, compacted_post);
-    
-        // Pretend to do some work. Sleeping would be too easy, as the background reclaim group would use
-        // all that time.
-        //
-        // Use thread_cputime_clock to prevent overcommitted test machines from stealing CPU time
-        // and causing test failures.
-        auto deadline = thread_cputime_clock::now() + 100ms;
-        while (thread_cputime_clock::now() < deadline) {
-            thread::maybe_yield();
-        }
     }
 }
 
diff --git a/utils/logalloc.cc b/utils/logalloc.cc
index f57d639647..b94ba40f4b 100644
--- a/utils/logalloc.cc
+++ b/utils/logalloc.cc
@@ -405,7 +405,7 @@ class background_reclaimer {
     promise<>* _main_loop_wait = nullptr;
     future<> _done;
     bool _stopping = false;
-    static constexpr size_t free_memory_threshold = 60'000'000;
+    static constexpr size_t free_memory_threshold = background_reclaim_free_memory_threshold;
 private:
     bool have_work() const {
 #ifndef SEASTAR_DEFAULT_ALLOCATOR
diff --git a/utils/logalloc.hh b/utils/logalloc.hh
index 1685adff4b..21e11e6440 100644
--- a/utils/logalloc.hh
+++ b/utils/logalloc.hh
@@ -29,6 +29,8 @@ constexpr int segment_size_shift = 17; // 128K; see #151, #152
 constexpr size_t segment_size = 1 << segment_size_shift;
 constexpr size_t max_zone_segments = 256;
 
+constexpr size_t background_reclaim_free_memory_threshold = 60'000'000;
+
 //
 // Frees some amount of objects from the region to which it's attached.
 //