diff --git a/src/gradient_free_optimizers/optimizers/local_opt/hill_climbing_optimizer.py b/src/gradient_free_optimizers/optimizers/local_opt/hill_climbing_optimizer.py
index f1e1354d..879c3a3f 100644
--- a/src/gradient_free_optimizers/optimizers/local_opt/hill_climbing_optimizer.py
+++ b/src/gradient_free_optimizers/optimizers/local_opt/hill_climbing_optimizer.py
@@ -191,8 +191,8 @@ def _iterate_discrete_batch(self) -> ndarray:
         max_positions = bounds[:, 1]
         sigmas = max_positions * self.epsilon
 
-        # Prevent zero sigma for single-value dimensions
-        sigmas = maximum(sigmas, 1e-10)
+        # Prevent getting stuck: ensure noise standard deviation is at least 1.0 index
+        sigmas = maximum(sigmas, 1.0)
 
         # Generate noise using the configured distribution
         noise_fn = self._DISTRIBUTIONS[self.distribution]