diff --git a/src/backends/cuda/active_set_system/global_active_set_manager.cu b/src/backends/cuda/active_set_system/global_active_set_manager.cu
index 26525460..1bf754ad 100644
--- a/src/backends/cuda/active_set_system/global_active_set_manager.cu
+++ b/src/backends/cuda/active_set_system/global_active_set_manager.cu
@@ -819,6 +819,11 @@ Float GlobalActiveSetManager::toi_threshold() const
     return m_impl.toi_threshold;
 }
 
+Float GlobalActiveSetManager::alpha_lower_bound() const
+{
+    return m_impl.alpha_lower_bound;
+}
+
 GlobalActiveSetManager::NonPenetratePositionInfo::NonPenetratePositionInfo(Impl* impl,
                                                                            SizeT offset,
                                                                            SizeT count) noexcept
@@ -855,6 +860,7 @@ void GlobalActiveSetManager::Impl::init(WorldVisitor& world)
     dt           = config.find<Float>("dt")->view()[0];
     decay_factor = config.find<Float>("contact/al-ipc/decay_factor")->view()[0];
     toi_threshold = config.find<Float>("contact/al-ipc/toi_threshold")->view()[0];
+    alpha_lower_bound = config.find<Float>("contact/al-ipc/alpha_lower_bound")->view()[0];
     energy_enabled = true;
 }
 
diff --git a/src/backends/cuda/active_set_system/global_active_set_manager.h b/src/backends/cuda/active_set_system/global_active_set_manager.h
index 6868e676..437c1e02 100644
--- a/src/backends/cuda/active_set_system/global_active_set_manager.h
+++ b/src/backends/cuda/active_set_system/global_active_set_manager.h
@@ -108,6 +108,7 @@ class GlobalActiveSetManager final : public SimSystem
 
         Float decay_factor, dt;
         Float toi_threshold;
+        Float alpha_lower_bound;
         bool  energy_enabled;
         bool  should_discard_friction_candidates = false;
 
@@ -168,6 +169,7 @@ class GlobalActiveSetManager final : public SimSystem
     //tex: $\Gamma$
     Float decay_factor() const;
     Float toi_threshold() const;
+    Float alpha_lower_bound() const;
     bool  is_enabled() const;
 
   protected:
diff --git a/src/backends/cuda/engine/advance_al.cu b/src/backends/cuda/engine/advance_al.cu
index f5e21806..367d44cc 100644
--- a/src/backends/cuda/engine/advance_al.cu
+++ b/src/backends/cuda/engine/advance_al.cu
@@ -410,7 +410,8 @@ void SimEngine::advance_AL()
                     m_global_active_set_manager->update_active_set();
                     m_global_active_set_manager->post_ccd();
 
-                    m_global_active_set_manager->advance_non_penetrate_positions(alpha);
+                    if(alpha > m_global_active_set_manager->alpha_lower_bound())
+                        m_global_active_set_manager->advance_non_penetrate_positions(alpha);
                 }
 
                 // Update alpha and beta for next iteration
diff --git a/src/core/core/scene_default_config.cpp b/src/core/core/scene_default_config.cpp
index 0d8d6711..2a6a211e 100644
--- a/src/core/core/scene_default_config.cpp
+++ b/src/core/core/scene_default_config.cpp
@@ -52,6 +52,7 @@ geometry::AttributeCollection default_scene_config() noexcept
     config.create("contact/al-ipc/mu_scale_fem", Float{5e7});
     config.create("contact/al-ipc/mu_scale_abd", Float{1e5});
     config.create("contact/al-ipc/toi_threshold", Float{0.1});
+    config.create("contact/al-ipc/alpha_lower_bound", Float{1e-6});
     config.create("contact/al-ipc/decay_factor", Float{0.3});
 
     // adaptive contact tuning knobs.