diff --git a/llama.cpp b/llama.cpp
index a528eef4a..ac22a48f8 100644
--- a/llama.cpp
+++ b/llama.cpp
@@ -2015,9 +2015,10 @@ void llama_sample_top_p(struct llama_context * ctx, llama_token_data_array * can
     for (size_t i = 0; i < candidates->size; ++i) {
         cum_sum += candidates->data[i].p;
 
-        // Check if the running sum is greater than p or if we have kept at least min_keep tokens
-        if (cum_sum > p && i >= min_keep) {
-            last_idx = i;
+        // Check if the running sum is at least p or if we have kept at least min_keep tokens
+        // we set the last index to i+1 to indicate that the current iterate should be included in the set
+        if (cum_sum >= p && i + 1 >= min_keep) {
+            last_idx = i + 1;
             break;
         }
     }
diff --git a/tests/test-sampling.cpp b/tests/test-sampling.cpp
index 5d693f7b5..64f9455d7 100644
--- a/tests/test-sampling.cpp
+++ b/tests/test-sampling.cpp
@@ -181,6 +181,7 @@ int main(void) {
 
     test_top_p({0.1f, 0.2f, 0.3f, 0.4f}, {0.4f}, 0);
     test_top_p({0.1f, 0.2f, 0.3f, 0.4f}, {0.4f, 0.3f}, 0.7f);
+    test_top_p({0.1f, 0.2f, 0.3f, 0.4f}, {0.4f, 0.3f, 0.2f}, 0.8f);
     test_top_p({0.1f, 0.2f, 0.3f, 0.4f}, {0.4f, 0.3f, 0.2f, 0.1f}, 1);
 
     test_tfs({0.1f, 0.15f, 0.2f, 0.25f, 0.3f}, {0.3f}, 0.25f);