diff --git a/common/speculative.cpp b/common/speculative.cpp
index 318e96ea3..b1fff27a5 100644
--- a/common/speculative.cpp
+++ b/common/speculative.cpp
@@ -252,11 +252,6 @@ llama_tokens common_speculative_gen_draft(
         // add drafted token for each sequence
         const llama_token id = cur_p->data[0].id;
 
-        // only collect very high-confidence draft tokens
-        if (cur_p->data[0].p < params.p_min) {
-            break;
-        }
-
         common_sampler_accept(smpl, id, true);
 
         result.push_back(id);
@@ -265,6 +260,11 @@ llama_tokens common_speculative_gen_draft(
             break;
         }
 
+        // only collect very high-confidence draft tokens
+        if (cur_p->data[0].p < params.p_min) {
+            break;
+        }
+
         common_batch_add(batch, id, n_past + i + 1, { 0 }, true);
 
         // evaluate the drafted tokens on the draft model
diff --git a/examples/server/server.cpp b/examples/server/server.cpp
index 809bfe0e3..2306dc26f 100644
--- a/examples/server/server.cpp
+++ b/examples/server/server.cpp
@@ -274,7 +274,7 @@ struct server_task {
         params.speculative.p_min = json_value(data, "speculative.p_min", defaults.speculative.p_min);
 
         params.speculative.n_min = std::min(params.speculative.n_max, params.speculative.n_min);
-        params.speculative.n_min = std::max(params.speculative.n_min, 2);
+        params.speculative.n_min = std::max(params.speculative.n_min, 0);
         params.speculative.n_max = std::max(params.speculative.n_max, 0);
 
         // Use OpenAI API logprobs only if n_probs wasn't provided