diff --git a/src/bitmap.c b/src/bitmap.c
index bdd1c869..98b53052 100644
--- a/src/bitmap.c
+++ b/src/bitmap.c
@@ -11,7 +11,6 @@ represeted as an array of fields where each field is a machine word (`size_t`)
 
 There are two api's; the standard one cannot have sequences that cross
 between the bitmap fields (and a sequence must be <= MI_BITMAP_FIELD_BITS).
-(this is used in region allocation)
 
 The `_across` postfixed functions do allow sequences that can cross over
 between the fields. (This is used in arena allocation)
@@ -63,12 +62,12 @@ bool _mi_bitmap_try_find_claim_field(mi_bitmap_t bitmap, size_t idx, const size_
 
   // scan linearly for a free range of zero bits
   while (bitidx <= bitidx_max) {
-    const size_t mapm = map & m;
+    const size_t mapm = (map & m);
     if (mapm == 0) {  // are the mask bits free at bitidx?
       mi_assert_internal((m >> bitidx) == mask); // no overflow?
-      const size_t newmap = map | m;
+      const size_t newmap = (map | m);
       mi_assert_internal((newmap^map) >> bitidx == mask);
-      if (!mi_atomic_cas_weak_acq_rel(field, &map, newmap)) {  // TODO: use strong cas here?
+      if (!mi_atomic_cas_strong_acq_rel(field, &map, newmap)) {  // TODO: use weak cas here?
         // no success, another thread claimed concurrently.. keep going (with updated `map`)
         continue;
       }
@@ -81,7 +80,8 @@ bool _mi_bitmap_try_find_claim_field(mi_bitmap_t bitmap, size_t idx, const size_
     else {
       // on to the next bit range
 #ifdef MI_HAVE_FAST_BITSCAN
-      const size_t shift = (count == 1 ? 1 : mi_bsr(mapm) - bitidx + 1);
+      mi_assert_internal(mapm != 0);
+      const size_t shift = (count == 1 ? 1 : (MI_INTPTR_BITS - mi_clz(mapm) - bitidx));
       mi_assert_internal(shift > 0 && shift <= count);
 #else
       const size_t shift = 1;
@@ -100,7 +100,7 @@ bool _mi_bitmap_try_find_claim_field(mi_bitmap_t bitmap, size_t idx, const size_
 bool _mi_bitmap_try_find_from_claim(mi_bitmap_t bitmap, const size_t bitmap_fields, const size_t start_field_idx, const size_t count, mi_bitmap_index_t* bitmap_idx) {
   size_t idx = start_field_idx;
   for (size_t visited = 0; visited < bitmap_fields; visited++, idx++) {
-    if (idx >= bitmap_fields) idx = 0; // wrap
+    if (idx >= bitmap_fields) { idx = 0; } // wrap
     if (_mi_bitmap_try_find_claim_field(bitmap, idx, count, bitmap_idx)) {
       return true;
     }
@@ -108,13 +108,6 @@ bool _mi_bitmap_try_find_from_claim(mi_bitmap_t bitmap, const size_t bitmap_fiel
   return false;
 }
 
-/*
-// Find `count` bits of 0 and set them to 1 atomically; returns `true` on success.
-// For now, `count` can be at most MI_BITMAP_FIELD_BITS and will never span fields.
-bool _mi_bitmap_try_find_claim(mi_bitmap_t bitmap, const size_t bitmap_fields, const size_t count, mi_bitmap_index_t* bitmap_idx) {
-  return _mi_bitmap_try_find_from_claim(bitmap, bitmap_fields, 0, count, bitmap_idx);
-}
-*/
 
 // Set `count` bits at `bitmap_idx` to 0 atomically
 // Returns `true` if all `count` bits were 1 previously.
@@ -124,7 +117,7 @@ bool _mi_bitmap_unclaim(mi_bitmap_t bitmap, size_t bitmap_fields, size_t count,
   const size_t mask = mi_bitmap_mask_(count, bitidx);
   mi_assert_internal(bitmap_fields > idx); MI_UNUSED(bitmap_fields);
   // mi_assert_internal((bitmap[idx] & mask) == mask);
-  size_t prev = mi_atomic_and_acq_rel(&bitmap[idx], ~mask);
+  const size_t prev = mi_atomic_and_acq_rel(&bitmap[idx], ~mask);
   return ((prev & mask) == mask);
 }
 
@@ -138,7 +131,7 @@ bool _mi_bitmap_claim(mi_bitmap_t bitmap, size_t bitmap_fields, size_t count, mi
   mi_assert_internal(bitmap_fields > idx); MI_UNUSED(bitmap_fields);
   //mi_assert_internal(any_zero != NULL || (bitmap[idx] & mask) == 0);
   size_t prev = mi_atomic_or_acq_rel(&bitmap[idx], mask);
-  if (any_zero != NULL) *any_zero = ((prev & mask) != mask);
+  if (any_zero != NULL) { *any_zero = ((prev & mask) != mask); }
   return ((prev & mask) == 0);
 }
 
@@ -148,8 +141,8 @@ static bool mi_bitmap_is_claimedx(mi_bitmap_t bitmap, size_t bitmap_fields, size
   const size_t bitidx = mi_bitmap_index_bit_in_field(bitmap_idx);
   const size_t mask = mi_bitmap_mask_(count, bitidx);
   mi_assert_internal(bitmap_fields > idx); MI_UNUSED(bitmap_fields);
-  size_t field = mi_atomic_load_relaxed(&bitmap[idx]);
-  if (any_ones != NULL) *any_ones = ((field & mask) != 0);
+  const size_t field = mi_atomic_load_relaxed(&bitmap[idx]);
+  if (any_ones != NULL) { *any_ones = ((field & mask) != 0); }
   return ((field & mask) == mask);
 }
 
@@ -160,10 +153,13 @@ bool _mi_bitmap_try_claim(mi_bitmap_t bitmap, size_t bitmap_fields, size_t count
   const size_t bitidx = mi_bitmap_index_bit_in_field(bitmap_idx);
   const size_t mask = mi_bitmap_mask_(count, bitidx);
   mi_assert_internal(bitmap_fields > idx); MI_UNUSED(bitmap_fields);
-  size_t expected = 0;
-  if (mi_atomic_cas_strong_acq_rel(&bitmap[idx], &expected, mask)) return true;
-  if ((expected & mask) != 0) return false;
-  return mi_atomic_cas_strong_acq_rel(&bitmap[idx], &expected, expected | mask);
+  size_t expected = mi_atomic_load_relaxed(&bitmap[idx]);
+  do  {    
+    if ((expected & mask) != 0) return false;
+  } 
+  while (!mi_atomic_cas_strong_acq_rel(&bitmap[idx], &expected, expected | mask));
+  mi_assert_internal((expected & mask) == 0);
+  return true;
 }
 
 
@@ -185,6 +181,7 @@ bool _mi_bitmap_is_any_claimed(mi_bitmap_t bitmap, size_t bitmap_fields, size_t
 
 // Try to atomically claim a sequence of `count` bits starting from the field
 // at `idx` in `bitmap` and crossing into subsequent fields. Returns `true` on success.
+// Only needs to consider crossing into the next fields (see `mi_bitmap_try_find_from_claim_across`)
 static bool mi_bitmap_try_find_claim_field_across(mi_bitmap_t bitmap, size_t bitmap_fields, size_t idx, const size_t count, const size_t retries, mi_bitmap_index_t* bitmap_idx)
 {
   mi_assert_internal(bitmap_idx != NULL);
@@ -195,9 +192,9 @@ static bool mi_bitmap_try_find_claim_field_across(mi_bitmap_t bitmap, size_t bit
   const size_t initial = mi_clz(map);  // count of initial zeros starting at idx
   mi_assert_internal(initial <= MI_BITMAP_FIELD_BITS);
   if (initial == 0)     return false;
-  if (initial >= count) return _mi_bitmap_try_find_claim_field(bitmap, idx, count, bitmap_idx);     // no need to cross fields
+  if (initial >= count) return _mi_bitmap_try_find_claim_field(bitmap, idx, count, bitmap_idx);    // no need to cross fields (this case won't happen for us)
   if (_mi_divide_up(count - initial, MI_BITMAP_FIELD_BITS) >= (bitmap_fields - idx)) return false; // not enough entries
-
+  
   // scan ahead
   size_t found = initial;
   size_t mask = 0;     // mask bits for the final field
@@ -205,25 +202,27 @@ static bool mi_bitmap_try_find_claim_field_across(mi_bitmap_t bitmap, size_t bit
     field++;
     map = mi_atomic_load_relaxed(field);
     const size_t mask_bits = (found + MI_BITMAP_FIELD_BITS <= count ? MI_BITMAP_FIELD_BITS : (count - found));
+    mi_assert_internal(mask_bits > 0 && mask_bits <= MI_BITMAP_FIELD_BITS);
     mask = mi_bitmap_mask_(mask_bits, 0);
-    if ((map & mask) != 0) return false;
+    if ((map & mask) != 0) return false;  // some part is already claimed
     found += mask_bits;
   }
   mi_assert_internal(field < &bitmap[bitmap_fields]);
 
-  // found range of zeros up to the final field; mask contains mask in the final field
-  // now claim it atomically
+  // we found a range of contiguous zeros up to the final field; mask contains mask in the final field
+  // now try to claim the range atomically
   mi_bitmap_field_t* const final_field = field;
   const size_t final_mask = mask;
   mi_bitmap_field_t* const initial_field = &bitmap[idx];
-  const size_t initial_mask = mi_bitmap_mask_(initial, MI_BITMAP_FIELD_BITS - initial);
+  const size_t initial_idx = MI_BITMAP_FIELD_BITS - initial;
+  const size_t initial_mask = mi_bitmap_mask_(initial, initial_idx);
 
   // initial field
   size_t newmap;
   field = initial_field;
   map = mi_atomic_load_relaxed(field);
   do {
-    newmap = map | initial_mask;
+    newmap = (map | initial_mask);
     if ((map & initial_mask) != 0) { goto rollback; };
   } while (!mi_atomic_cas_strong_acq_rel(field, &map, newmap));
 
@@ -238,31 +237,32 @@ static bool mi_bitmap_try_find_claim_field_across(mi_bitmap_t bitmap, size_t bit
   mi_assert_internal(field == final_field);
   map = mi_atomic_load_relaxed(field);
   do {
-    newmap = map | final_mask;
+    newmap = (map | final_mask);
     if ((map & final_mask) != 0) { goto rollback; }
   } while (!mi_atomic_cas_strong_acq_rel(field, &map, newmap));
 
   // claimed!
-  *bitmap_idx = mi_bitmap_index_create(idx, MI_BITMAP_FIELD_BITS - initial);
+  *bitmap_idx = mi_bitmap_index_create(idx, initial_idx);
   return true;
 
 rollback:
   // roll back intermediate fields
+  // (we just failed to claim `field` so decrement first)
   while (--field > initial_field) {
     newmap = 0;
     map = mi_bitmap_mask_(MI_BITMAP_FIELD_BITS, 0);
     mi_assert_internal(mi_atomic_load_relaxed(field) == map);
     mi_atomic_store_release(field, newmap);
   }
-  if (field == initial_field) {
+  if (field == initial_field) {               // (if we failed on the initial field, `field + 1 == initial_field`)
     map = mi_atomic_load_relaxed(field);
     do {
       mi_assert_internal((map & initial_mask) == initial_mask);
-      newmap = map & ~initial_mask;
+      newmap = (map & ~initial_mask);
     } while (!mi_atomic_cas_strong_acq_rel(field, &map, newmap));
   }
   // retry? (we make a recursive call instead of goto to be able to use const declarations)
-  if (retries < 4) {
+  if (retries <= 2) {
     return mi_bitmap_try_find_claim_field_across(bitmap, bitmap_fields, idx, count, retries+1, bitmap_idx);
   }
   else {
@@ -275,17 +275,22 @@ rollback:
 // Starts at idx, and wraps around to search in all `bitmap_fields` fields.
 bool _mi_bitmap_try_find_from_claim_across(mi_bitmap_t bitmap, const size_t bitmap_fields, const size_t start_field_idx, const size_t count, mi_bitmap_index_t* bitmap_idx) {
   mi_assert_internal(count > 0);
-  if (count==1) return _mi_bitmap_try_find_from_claim(bitmap, bitmap_fields, start_field_idx, count, bitmap_idx);
+  if (count <= 2) {
+    // we don't bother with crossover fields for small counts
+    return _mi_bitmap_try_find_from_claim(bitmap, bitmap_fields, start_field_idx, count, bitmap_idx);
+  }
+
+  // visit the fields
   size_t idx = start_field_idx;
   for (size_t visited = 0; visited < bitmap_fields; visited++, idx++) {
-    if (idx >= bitmap_fields) idx = 0; // wrap
-    // try to claim inside the field
+    if (idx >= bitmap_fields) { idx = 0; } // wrap
+    // first try to claim inside a field
     if (count <= MI_BITMAP_FIELD_BITS) {
       if (_mi_bitmap_try_find_claim_field(bitmap, idx, count, bitmap_idx)) {
         return true;
       }
     }
-    // try to claim across fields
+    // if that fails, then try to claim across fields
     if (mi_bitmap_try_find_claim_field_across(bitmap, bitmap_fields, idx, count, 0, bitmap_idx)) {
       return true;
     }
@@ -328,14 +333,14 @@ bool _mi_bitmap_unclaim_across(mi_bitmap_t bitmap, size_t bitmap_fields, size_t
   size_t mid_count = mi_bitmap_mask_across(bitmap_idx, bitmap_fields, count, &pre_mask, &mid_mask, &post_mask);
   bool all_one = true;
   mi_bitmap_field_t* field = &bitmap[idx];
-  size_t prev = mi_atomic_and_acq_rel(field++, ~pre_mask);
+  size_t prev = mi_atomic_and_acq_rel(field++, ~pre_mask);   // clear first part
   if ((prev & pre_mask) != pre_mask) all_one = false;
   while(mid_count-- > 0) {
-    prev = mi_atomic_and_acq_rel(field++, ~mid_mask);
+    prev = mi_atomic_and_acq_rel(field++, ~mid_mask);        // clear mid part
     if ((prev & mid_mask) != mid_mask) all_one = false;
   }
   if (post_mask!=0) {
-    prev = mi_atomic_and_acq_rel(field, ~post_mask);
+    prev = mi_atomic_and_acq_rel(field, ~post_mask);         // clear end part
     if ((prev & post_mask) != post_mask) all_one = false;
   }
   return all_one;
@@ -365,7 +370,7 @@ bool _mi_bitmap_claim_across(mi_bitmap_t bitmap, size_t bitmap_fields, size_t co
     if ((prev & post_mask) != 0) all_zero = false;
     if ((prev & post_mask) != post_mask) any_zero = true;
   }
-  if (pany_zero != NULL) *pany_zero = any_zero;
+  if (pany_zero != NULL) { *pany_zero = any_zero; }
   return all_zero;
 }
 
@@ -394,7 +399,7 @@ static bool mi_bitmap_is_claimedx_across(mi_bitmap_t bitmap, size_t bitmap_field
     if ((prev & post_mask) != post_mask) all_ones = false;
     if ((prev & post_mask) != 0) any_ones = true;
   }
-  if (pany_ones != NULL) *pany_ones = any_ones;
+  if (pany_ones != NULL) { *pany_ones = any_ones; }
   return all_ones;
 }