diff --git a/python/sglang/srt/speculative/eagle_draft_extend_cuda_graph_runner.py b/python/sglang/srt/speculative/eagle_draft_extend_cuda_graph_runner.py
index 9df3742fcf28..e588422782b5 100644
--- a/python/sglang/srt/speculative/eagle_draft_extend_cuda_graph_runner.py
+++ b/python/sglang/srt/speculative/eagle_draft_extend_cuda_graph_runner.py
@@ -401,8 +401,14 @@ def run_once():
                 forward_batch.positions,
                 forward_batch,
             )
-            probs = torch.softmax(ret.next_token_logits, dim=-1)
-            ret.topk_p, ret.topk_index = fast_topk(probs, self.topk, dim=-1)
+            if self.topk == 1:
+                ret.topk_index = torch.argmax(
+                    ret.next_token_logits, dim=-1, keepdim=True
+                )
+                ret.topk_p = torch.ones_like(ret.topk_index, dtype=torch.float32)
+            else:
+                probs = torch.softmax(ret.next_token_logits, dim=-1)
+                ret.topk_p, ret.topk_index = fast_topk(probs, self.topk, dim=-1)
 
             forward_batch.out_cache_loc = output_cache_loc_backup
             forward_batch.spec_info.hidden_states = hidden_states_backup
diff --git a/python/sglang/srt/speculative/eagle_worker_v2.py b/python/sglang/srt/speculative/eagle_worker_v2.py
index a3d14af9122b..56d41ebcc1de 100644
--- a/python/sglang/srt/speculative/eagle_worker_v2.py
+++ b/python/sglang/srt/speculative/eagle_worker_v2.py
@@ -479,8 +479,16 @@ def draft_forward(self, forward_batch: ForwardBatch):
                     forward_batch, skip_attn_backend_init=True
                 ).logits_output
             maybe_detect_nan(logits_output.next_token_logits, f"draft_forward step {i}")
-            probs = torch.softmax(logits_output.next_token_logits, dim=-1)
-            topk_p, topk_index = fast_topk(probs, self.topk, dim=-1)
+            if self.topk == 1:
+                # topk=1 → degenerate single-path tree; `topk_p` is unused
+                # downstream, so skip softmax and just argmax over logits.
+                topk_index = torch.argmax(
+                    logits_output.next_token_logits, dim=-1, keepdim=True
+                )
+                topk_p = torch.ones_like(topk_index, dtype=torch.float32)
+            else:
+                probs = torch.softmax(logits_output.next_token_logits, dim=-1)
+                topk_p, topk_index = fast_topk(probs, self.topk, dim=-1)
             maybe_detect_oob(
                 topk_index,
                 0,
@@ -647,8 +655,14 @@ def _draft_extend_for_decode(
             draft_logits_output.hidden_states = draft_logits_output.hidden_states[
                 select_index
             ]
-        probs = torch.softmax(draft_logits_output.next_token_logits, dim=-1)
-        ret_topk_p, ret_topk_index = fast_topk(probs, self.topk, dim=-1)
+        if self.topk == 1:
+            ret_topk_index = torch.argmax(
+                draft_logits_output.next_token_logits, dim=-1, keepdim=True
+            )
+            ret_topk_p = torch.ones_like(ret_topk_index, dtype=torch.float32)
+        else:
+            probs = torch.softmax(draft_logits_output.next_token_logits, dim=-1)
+            ret_topk_p, ret_topk_index = fast_topk(probs, self.topk, dim=-1)
         ret_hidden_states = draft_logits_output.hidden_states
 
         # Construct the return values