diff --git a/crates/tinymemory-integrations/src/cortex/testing/mod.rs b/crates/tinymemory-integrations/src/cortex/testing/mod.rs
index 2efba3ee..223796fd 100644
--- a/crates/tinymemory-integrations/src/cortex/testing/mod.rs
+++ b/crates/tinymemory-integrations/src/cortex/testing/mod.rs
@@ -174,9 +174,13 @@ pub(crate) type Shared = Arc<Double>;
 
 /// Decrements `counter` if positive; whether a unit was taken.
 pub(crate) fn take_one(counter: &AtomicUsize) -> bool {
-    counter
+    // `fetch_update` is deprecated for `try_update` on newer toolchains, which
+    // is not stable on this crate's MSRV.
+    #[allow(deprecated)]
+    let taken = counter
         .fetch_update(Ordering::SeqCst, Ordering::SeqCst, |n| n.checked_sub(1))
-        .is_ok()
+        .is_ok();
+    taken
 }
 
 impl Double {
diff --git a/crates/tinymemory-tools/src/deletion/mod_tests.rs b/crates/tinymemory-tools/src/deletion/mod_tests.rs
index 55a9cdc8..946db09b 100644
--- a/crates/tinymemory-tools/src/deletion/mod_tests.rs
+++ b/crates/tinymemory-tools/src/deletion/mod_tests.rs
@@ -142,14 +142,16 @@ impl ListStore<PendingDeletion> for &Flaky {
     }
     fn save(&self, all: &[PendingDeletion]) -> Result<(), crate::list_store::StoreError> {
         let failing = &self.failing_saves;
-        if failing
+        // `fetch_update` is deprecated for `try_update` on newer toolchains, which is not stable on this crate's MSRV.
+        #[allow(deprecated)]
+        let taken = failing
             .fetch_update(
                 std::sync::atomic::Ordering::SeqCst,
                 std::sync::atomic::Ordering::SeqCst,
                 |left| left.checked_sub(1),
             )
-            .is_ok()
-        {
+            .is_ok();
+        if taken {
             return Err(crate::list_store::StoreError("full".into()));
         }
         self.saves.lock().unwrap().push(all.to_vec());
diff --git a/crates/tinymemory-tools/src/prefetch/mod.rs b/crates/tinymemory-tools/src/prefetch/mod.rs
index 33541fa5..167c8baa 100644
--- a/crates/tinymemory-tools/src/prefetch/mod.rs
+++ b/crates/tinymemory-tools/src/prefetch/mod.rs
@@ -74,14 +74,24 @@ impl WorkerPool {
     }
 
     fn try_acquire(&self) -> Option<Permit> {
-        self.free
-            .fetch_update(Ordering::AcqRel, Ordering::Acquire, |free| {
-                free.checked_sub(1)
-            })
-            .ok()
-            .map(|_| Permit {
-                free: self.free.clone(),
-            })
+        // A compare_exchange loop rather than `fetch_update`: that method is
+        // deprecated in favour of `try_update` on newer toolchains, but
+        // `try_update` is not stable on this crate's MSRV.
+        let mut free = self.free.load(Ordering::Acquire);
+        loop {
+            let next = free.checked_sub(1)?;
+            match self
+                .free
+                .compare_exchange_weak(free, next, Ordering::AcqRel, Ordering::Acquire)
+            {
+                Ok(_) => {
+                    return Some(Permit {
+                        free: self.free.clone(),
+                    });
+                }
+                Err(actual) => free = actual,
+            }
+        }
     }
 
     /// Workers not running a refresh.
diff --git a/crates/tinymemory-tools/src/prefetch/mod_tests.rs b/crates/tinymemory-tools/src/prefetch/mod_tests.rs
index c0e1a8a9..ae553cce 100644
--- a/crates/tinymemory-tools/src/prefetch/mod_tests.rs
+++ b/crates/tinymemory-tools/src/prefetch/mod_tests.rs
@@ -203,3 +203,22 @@ fn runtime_shutdown_releases_worker_and_pending_work() {
     assert_eq!(pool.available(), 1, "the permit is released");
     assert!(cache.completed(&"k").is_none());
 }
+
+#[test]
+fn concurrent_acquires_never_exceed_the_pool_size() {
+    let pool = WorkerPool::new(3);
+    let granted = std::sync::Mutex::new(Vec::new());
+    std::thread::scope(|scope| {
+        for _ in 0..16 {
+            scope.spawn(|| {
+                if let Some(permit) = pool.try_acquire() {
+                    granted.lock().unwrap().push(permit);
+                }
+            });
+        }
+    });
+    assert_eq!(granted.lock().unwrap().len(), 3);
+    assert_eq!(pool.available(), 0);
+    granted.lock().unwrap().clear();
+    assert_eq!(pool.available(), 3);
+}