diff --git a/c_api/impl/AuxIndexStructures_c.cpp b/c_api/impl/AuxIndexStructures_c.cpp
index c19c1b63be..ff78cc3525 100644
--- a/c_api/impl/AuxIndexStructures_c.cpp
+++ b/c_api/impl/AuxIndexStructures_c.cpp
@@ -88,6 +88,13 @@ int faiss_IDSelector_is_member(const FaissIDSelector* sel, idx_t id) {
     return reinterpret_cast<const IDSelector*>(sel)->is_member(id);
 }
 
+int faiss_IDSelector_is_member_with_dist(
+        const FaissIDSelector* sel,
+        idx_t id,
+        float dist) {
+    return reinterpret_cast<const IDSelector*>(sel)->is_member(id, dist);
+}
+
 DEFINE_DESTRUCTOR(IDSelectorRange)
 
 DEFINE_GETTER(IDSelectorRange, idx_t, imin)
diff --git a/c_api/impl/AuxIndexStructures_c.h b/c_api/impl/AuxIndexStructures_c.h
index dba3026980..cd1306b7fa 100644
--- a/c_api/impl/AuxIndexStructures_c.h
+++ b/c_api/impl/AuxIndexStructures_c.h
@@ -53,6 +53,10 @@ FAISS_DECLARE_CLASS(IDSelector)
 FAISS_DECLARE_DESTRUCTOR(IDSelector)
 
 int faiss_IDSelector_is_member(const FaissIDSelector* sel, idx_t id);
+int faiss_IDSelector_is_member_with_dist(
+        const FaissIDSelector* sel,
+        idx_t id,
+        float dist);
 
 /** remove ids between [imni, imax) */
 FAISS_DECLARE_CLASS(IDSelectorRange)
diff --git a/faiss/IndexIDMap.h b/faiss/IndexIDMap.h
index 2d16412301..0047dc4b26 100644
--- a/faiss/IndexIDMap.h
+++ b/faiss/IndexIDMap.h
@@ -122,6 +122,9 @@ struct IDSelectorTranslated : IDSelector {
     bool is_member(idx_t id) const override {
         return sel->is_member(id_map[id]);
     }
+    bool is_member(idx_t id, std::optional<float> d) const override {
+        return sel->is_member(id_map[id], d);
+    }
 };
 
 } // namespace faiss
diff --git a/faiss/impl/HNSW.cpp b/faiss/impl/HNSW.cpp
index 3ba5f72f68..38dbddb894 100644
--- a/faiss/impl/HNSW.cpp
+++ b/faiss/impl/HNSW.cpp
@@ -568,7 +568,7 @@ int search_from_candidates(
         idx_t v1 = candidates.ids[i];
         float d = candidates.dis[i];
         FAISS_ASSERT(v1 >= 0);
-        if (!sel || sel->is_member(v1)) {
+        if (!sel || sel->is_member(v1, d)) {
             if (d < threshold) {
                 if (res.add_result(d, v1)) {
                     threshold = res.threshold;
@@ -637,7 +637,7 @@ int search_from_candidates(
         threshold = res.threshold;
 
         auto add_to_heap = [&](const size_t idx, const float dis) {
-            if (!sel || sel->is_member(idx)) {
+            if (!sel || sel->is_member(idx, dis)) {
                 if (dis < threshold) {
                     if (res.add_result(dis, idx)) {
                         threshold = res.threshold;
diff --git a/faiss/impl/IDSelector.cpp b/faiss/impl/IDSelector.cpp
index e4a4bba967..214cf0413f 100644
--- a/faiss/impl/IDSelector.cpp
+++ b/faiss/impl/IDSelector.cpp
@@ -17,7 +17,8 @@ namespace faiss {
 IDSelectorRange::IDSelectorRange(idx_t imin, idx_t imax, bool assume_sorted)
         : imin(imin), imax(imax), assume_sorted(assume_sorted) {}
 
-bool IDSelectorRange::is_member(idx_t id) const {
+bool IDSelectorRange::is_member(idx_t id, std::optional<float> d) const {
+    (void)d;
     return id >= imin && id < imax;
 }
 
@@ -69,7 +70,8 @@ void IDSelectorRange::find_sorted_ids_bounds(
 
 IDSelectorArray::IDSelectorArray(size_t n, const idx_t* ids) : n(n), ids(ids) {}
 
-bool IDSelectorArray::is_member(idx_t id) const {
+bool IDSelectorArray::is_member(idx_t id, std::optional<float> d) const {
+    (void)d;
     for (idx_t i = 0; i < n; i++) {
         if (ids[i] == id)
             return true;
@@ -99,7 +101,8 @@ IDSelectorBatch::IDSelectorBatch(size_t n, const idx_t* indices) {
     }
 }
 
-bool IDSelectorBatch::is_member(idx_t i) const {
+bool IDSelectorBatch::is_member(idx_t i, std::optional<float> d) const {
+    (void)d;
     long im = i & mask;
     if (!(bloom[im >> 3] & (1 << (im & 7)))) {
         return 0;
@@ -114,7 +117,8 @@ bool IDSelectorBatch::is_member(idx_t i) const {
 IDSelectorBitmap::IDSelectorBitmap(size_t n, const uint8_t* bitmap)
         : n(n), bitmap(bitmap) {}
 
-bool IDSelectorBitmap::is_member(idx_t ii) const {
+bool IDSelectorBitmap::is_member(idx_t ii, std::optional<float> d) const {
+    (void)d;
     uint64_t i = ii;
     if ((i >> 3) >= n) {
         return false;
diff --git a/faiss/impl/IDSelector.h b/faiss/impl/IDSelector.h
index 7760d2a9fa..de8b6aa185 100644
--- a/faiss/impl/IDSelector.h
+++ b/faiss/impl/IDSelector.h
@@ -7,6 +7,7 @@
 
 #pragma once
 
+#include <optional>
 #include <unordered_set>
 #include <vector>
 
@@ -19,7 +20,14 @@ namespace faiss {
 
 /** Encapsulates a set of ids to handle. */
 struct IDSelector {
-    virtual bool is_member(idx_t id) const = 0;
+    virtual bool is_member(idx_t id) const {
+        (void)id;
+        return true;
+    }
+    virtual bool is_member(idx_t id, std::optional<float> d) const {
+        (void)d;
+        return is_member(id);
+    }
     virtual ~IDSelector() {}
 };
 
@@ -33,7 +41,10 @@ struct IDSelectorRange : IDSelector {
 
     IDSelectorRange(idx_t imin, idx_t imax, bool assume_sorted = false);
 
-    bool is_member(idx_t id) const final;
+    bool is_member(idx_t id) const final {
+        return is_member(id, std::nullopt);
+    }
+    bool is_member(idx_t id, std::optional<float> d) const final;
 
     /// for sorted ids, find the range of list indices where the valid ids are
     /// stored
@@ -62,7 +73,10 @@ struct IDSelectorArray : IDSelector {
      *            IDSelectorArray's lifetime
      */
     IDSelectorArray(size_t n, const idx_t* ids);
-    bool is_member(idx_t id) const final;
+    bool is_member(idx_t id) const final {
+        return is_member(id, std::nullopt);
+    }
+    bool is_member(idx_t id, std::optional<float> d) const final;
     ~IDSelectorArray() override {}
 };
 
@@ -92,7 +106,10 @@ struct IDSelectorBatch : IDSelector {
      *            construction
      */
     IDSelectorBatch(size_t n, const idx_t* indices);
-    bool is_member(idx_t id) const final;
+    bool is_member(idx_t id) const final {
+        return is_member(id, std::nullopt);
+    }
+    bool is_member(idx_t id, std::optional<float> d) const final;
     ~IDSelectorBatch() override {}
 };
 
@@ -109,7 +126,10 @@ struct IDSelectorBitmap : IDSelector {
      *               (i%8) of bitmap[floor(i / 8)] is 1.
      */
     IDSelectorBitmap(size_t n, const uint8_t* bitmap);
-    bool is_member(idx_t id) const final;
+    bool is_member(idx_t id) const final {
+        return is_member(id, std::nullopt);
+    }
+    bool is_member(idx_t id, std::optional<float> d) const final;
     ~IDSelectorBitmap() override {}
 };
 
@@ -120,12 +140,21 @@ struct IDSelectorNot : IDSelector {
     bool is_member(idx_t id) const final {
         return !sel->is_member(id);
     }
+    bool is_member(idx_t id, std::optional<float> d) const final {
+        return !sel->is_member(id, d);
+    }
     virtual ~IDSelectorNot() {}
 };
 
 /// selects all entries (useful for benchmarking)
 struct IDSelectorAll : IDSelector {
     bool is_member(idx_t id) const final {
+        (void)id;
+        return true;
+    }
+    bool is_member(idx_t id, std::optional<float> d) const final {
+        (void)id;
+        (void)d;
         return true;
     }
     virtual ~IDSelectorAll() {}
@@ -141,6 +170,9 @@ struct IDSelectorAnd : IDSelector {
     bool is_member(idx_t id) const final {
         return lhs->is_member(id) && rhs->is_member(id);
     }
+    bool is_member(idx_t id, std::optional<float> d) const final {
+        return lhs->is_member(id, d) && rhs->is_member(id, d);
+    }
     virtual ~IDSelectorAnd() {}
 };
 
@@ -154,6 +186,9 @@ struct IDSelectorOr : IDSelector {
     bool is_member(idx_t id) const final {
         return lhs->is_member(id) || rhs->is_member(id);
     }
+    bool is_member(idx_t id, std::optional<float> d) const final {
+        return lhs->is_member(id, d) || rhs->is_member(id, d);
+    }
     virtual ~IDSelectorOr() {}
 };
 
@@ -167,6 +202,9 @@ struct IDSelectorXOr : IDSelector {
     bool is_member(idx_t id) const final {
         return lhs->is_member(id) ^ rhs->is_member(id);
     }
+    bool is_member(idx_t id, std::optional<float> d) const final {
+        return lhs->is_member(id, d) ^ rhs->is_member(id, d);
+    }
     virtual ~IDSelectorXOr() {}
 };
 
diff --git a/faiss/impl/ResultHandler.h b/faiss/impl/ResultHandler.h
index 3116eb24df..f65025fee4 100644
--- a/faiss/impl/ResultHandler.h
+++ b/faiss/impl/ResultHandler.h
@@ -19,6 +19,7 @@
 
 #include <algorithm>
 #include <iostream>
+#include <optional>
 
 namespace faiss {
 
@@ -62,8 +63,8 @@ struct BlockResultHandler {
 
     virtual ~BlockResultHandler() {}
 
-    bool is_in_selection(idx_t i) const {
-        return !use_sel || sel->is_member(i);
+    bool is_in_selection(idx_t i, std::optional<float> d = std::nullopt) const {
+        return !use_sel || sel->is_member(i, d);
     }
 };
 
diff --git a/faiss/impl/simd_result_handlers.h b/faiss/impl/simd_result_handlers.h
index 2fa18fa340..ee5d755d65 100644
--- a/faiss/impl/simd_result_handlers.h
+++ b/faiss/impl/simd_result_handlers.h
@@ -271,8 +271,8 @@ struct SingleResultHandler : ResultHandlerCompare<C, with_id_map> {
                 int j = __builtin_ctz(lt_mask);
                 auto real_idx = this->adjust_id(b, j);
                 lt_mask -= 1 << j;
-                if (this->sel->is_member(real_idx)) {
-                    T d = d32tab[j];
+                T d = d32tab[j];
+                if (this->sel->is_member(real_idx, d)) {
                     if (C::cmp(idis[q], d)) {
                         idis[q] = d;
                         ids[q] = real_idx;
@@ -367,8 +367,8 @@ struct HeapHandler : ResultHandlerCompare<C, with_id_map> {
                 int j = __builtin_ctz(lt_mask);
                 auto real_idx = this->adjust_id(b, j);
                 lt_mask -= 1 << j;
-                if (this->sel->is_member(real_idx)) {
-                    T dis = d32tab[j];
+                T dis = d32tab[j];
+                if (this->sel->is_member(real_idx, dis)) {
                     if (C::cmp(heap_dis[0], dis)) {
                         heap_replace_top<C>(
                                 k, heap_dis, heap_ids, dis, real_idx);
@@ -479,8 +479,8 @@ struct ReservoirHandler : ResultHandlerCompare<C, with_id_map> {
                 int j = __builtin_ctz(lt_mask);
                 auto real_idx = this->adjust_id(b, j);
                 lt_mask -= 1 << j;
-                if (this->sel->is_member(real_idx)) {
-                    T dis = d32tab[j];
+                T dis = d32tab[j];
+                if (this->sel->is_member(real_idx, dis)) {
                     res.add(dis, real_idx);
                 }
             }
@@ -602,8 +602,8 @@ struct RangeHandler : ResultHandlerCompare<C, with_id_map> {
                 lt_mask -= 1 << j;
 
                 auto real_idx = this->adjust_id(b, j);
-                if (this->sel->is_member(real_idx)) {
-                    T dis = d32tab[j];
+                T dis = d32tab[j];
+                if (this->sel->is_member(real_idx, dis)) {
                     n_per_query[q]++;
                     triplets.push_back({idx_t(q + q0), real_idx, dis});
                 }
diff --git a/faiss/python/python_callbacks.cpp b/faiss/python/python_callbacks.cpp
index 06b5c18cfc..62d4a31382 100644
--- a/faiss/python/python_callbacks.cpp
+++ b/faiss/python/python_callbacks.cpp
@@ -130,6 +130,24 @@ bool PyCallbackIDSelector::is_member(faiss::idx_t id) const {
     return b;
 }
 
+bool PyCallbackIDSelector::is_member(faiss::idx_t id, std::optional<float> d)
+        const {
+    if (!d.has_value()) {
+        return is_member(id);
+    }
+
+    FAISS_THROW_IF_NOT((id >> 32) == 0);
+    PyThreadLock gil;
+    PyObject* result =
+            PyObject_CallFunction(callback, "(nf)", int(id), d.value());
+    if (result == nullptr) {
+        FAISS_THROW_MSG("propagate py error");
+    }
+    bool b = PyObject_IsTrue(result);
+    Py_DECREF(result);
+    return b;
+}
+
 PyCallbackIDSelector::~PyCallbackIDSelector() {
     PyThreadLock gil;
     Py_DECREF(callback);
diff --git a/faiss/python/python_callbacks.h b/faiss/python/python_callbacks.h
index 421239bd0f..f3af0fa1c0 100644
--- a/faiss/python/python_callbacks.h
+++ b/faiss/python/python_callbacks.h
@@ -55,6 +55,7 @@ struct PyCallbackIDSelector : faiss::IDSelector {
     explicit PyCallbackIDSelector(PyObject* callback);
 
     bool is_member(faiss::idx_t id) const override;
+    bool is_member(faiss::idx_t id, std::optional<float> d) const override;
 
     ~PyCallbackIDSelector() override;
 };
diff --git a/faiss/utils/distances.cpp b/faiss/utils/distances.cpp
index 1506bee5cf..99d7ab413a 100644
--- a/faiss/utils/distances.cpp
+++ b/faiss/utils/distances.cpp
@@ -157,6 +157,9 @@ void exhaustive_inner_product_seq(
                     continue;
                 }
                 float ip = fvec_inner_product(x_i, y_j, d);
+                if (!res.is_in_selection(j, ip)) {
+                    continue;
+                }
                 resi.add_result(ip, j);
             }
             resi.end();
@@ -189,6 +192,9 @@ void exhaustive_L2sqr_seq(
                     continue;
                 }
                 float disij = fvec_L2sqr(x_i, y_j, d);
+                if (!res.is_in_selection(j, disij)) {
+                    continue;
+                }
                 resi.add_result(disij, j);
             }
             resi.end();