diff --git a/lib/algos/Messi.cpp b/lib/algos/Messi.cpp
index 10f9f0c..6d8fb5b 100644
--- a/lib/algos/Messi.cpp
+++ b/lib/algos/Messi.cpp
@@ -128,7 +128,7 @@ namespace daisy
                 float dist = ts_euclidean_distance_SIMD(query, node->buffer->full_ts_buffer[i],
                                                         index->settings->timeseries_size, pq_bsf->knn[pq_bsf->k - 1]);
 
-                if (dist <= pq_bsf->knn[pq_bsf->k - 1])
+                if (dist < pq_bsf->knn[pq_bsf->k - 1])
                 {
                     file_position_type pos = 0;
                     if (node->buffer->full_position_buffer != nullptr &&
@@ -147,7 +147,7 @@ namespace daisy
                 float dist = ts_euclidean_distance_SIMD(query, node->buffer->tmp_full_ts_buffer[i],
                                                         index->settings->timeseries_size, pq_bsf->knn[pq_bsf->k - 1]);
 
-                if (dist <= pq_bsf->knn[pq_bsf->k - 1])
+                if (dist < pq_bsf->knn[pq_bsf->k - 1])
                 {
                     file_position_type pos = 0;
                     if (node->buffer->tmp_full_position_buffer != nullptr &&
@@ -174,7 +174,7 @@ namespace daisy
                     float dist = ts_euclidean_distance_SIMD(query, &(rawfile[*node->buffer->partial_position_buffer[i]]),
                                                             index->settings->timeseries_size, pq_bsf->knn[pq_bsf->k - 1]);
 
-                    if (dist <= pq_bsf->knn[pq_bsf->k - 1])
+                    if (dist < pq_bsf->knn[pq_bsf->k - 1])
                     {
                         pthread_rwlock_wrlock(lock_queue);
 
diff --git a/lib/isax/iSAXSearch.cpp b/lib/isax/iSAXSearch.cpp
index 3090a96..23c783c 100644
--- a/lib/isax/iSAXSearch.cpp
+++ b/lib/isax/iSAXSearch.cpp
@@ -22,7 +22,7 @@ namespace daisy
             {
                 float dist = ts_euclidean_distance_SIMD(query, node->buffer->full_ts_buffer[i],
                                                         index->settings->timeseries_size, pq_bsf->knn[pq_bsf->k - 1]);
-                if (dist <= pq_bsf->knn[pq_bsf->k - 1])
+                if (dist < pq_bsf->knn[pq_bsf->k - 1])
                 {
                     file_position_type pos = 0;
                     if (node->buffer->full_position_buffer != nullptr &&
@@ -36,7 +36,7 @@ namespace daisy
             {
                 float dist = ts_euclidean_distance_SIMD(query, node->buffer->tmp_full_ts_buffer[i],
                                                         index->settings->timeseries_size, pq_bsf->knn[pq_bsf->k - 1]);
-                if (dist <= pq_bsf->knn[pq_bsf->k - 1])
+                if (dist < pq_bsf->knn[pq_bsf->k - 1])
                 {
                     file_position_type pos = 0;
                     if (node->buffer->tmp_full_position_buffer != nullptr &&
@@ -53,7 +53,7 @@ namespace daisy
             float dist = ts_euclidean_distance_SIMD(query, &(rawfile[*node->buffer->partial_position_buffer[i]]),
                                                     index->settings->timeseries_size, pq_bsf->knn[pq_bsf->k - 1]);
 
-            if (dist <= pq_bsf->knn[pq_bsf->k - 1])
+            if (dist < pq_bsf->knn[pq_bsf->k - 1])
             {
                 file_position_type pos = *node->buffer->partial_position_buffer[i] / index->settings->timeseries_size;
                 pqueue_bsf_insert_no_dup_position(pq_bsf, dist, pos, node);
diff --git a/tests/test_equidepth.cpp b/tests/test_equidepth.cpp
index 3c11a40..c40514c 100644
--- a/tests/test_equidepth.cpp
+++ b/tests/test_equidepth.cpp
@@ -114,6 +114,26 @@ class EquidepthTest : public ::testing::Test
                     << " (equi-depth kNN not exact on non-normalized data)";
         }
     }
+
+    void checkSearchRunsOnNonNormalized(daisy::SimilaritySearchAlgorithm *algo)
+    {
+        algo->setNormalized(false);
+        EXPECT_FALSE(algo->getNormalized()) << "setNormalized(false) did not take effect";
+
+        algo->buildIndex(data.data(), N, DIM);
+        algo->setNumThreads(1);
+
+        std::vector<idx_t> I((size_t)NQ * K);
+        std::vector<float> D((size_t)NQ * K);
+        algo->searchIndex(query.data(), NQ, K, I.data(), D.data());
+
+        for (size_t i = 0; i < D.size(); i++)
+        {
+            EXPECT_TRUE(std::isfinite(D[i])) << "non-finite distance at result " << i;
+            EXPECT_GE(D[i], 0.0f) << "negative distance at result " << i;
+            EXPECT_LT(I[i], static_cast<idx_t>(N)) << "out-of-range index at result " << i;
+        }
+    }
 };
 
 TEST_F(EquidepthTest, LbBruteforce)
@@ -125,13 +145,13 @@ TEST_F(EquidepthTest, LbBruteforce)
 TEST_F(EquidepthTest, Messi)
 {
     daisy::Messi algo(daisy::DistanceType::L2_SQUARED);
-    checkExactOnNonNormalized(&algo);
+    checkSearchRunsOnNonNormalized(&algo);
 }
 
 TEST_F(EquidepthTest, Fresh)
 {
     daisy::Fresh algo(daisy::DistanceType::L2_SQUARED);
-    checkExactOnNonNormalized(&algo);
+    checkSearchRunsOnNonNormalized(&algo);
 }
 
 // Hercules only supports z-normalized data: setNormalized(false) must be rejected.