diff --git a/interface/src/LODManager.cpp b/interface/src/LODManager.cpp
index d3c8746e16..01ccbd0d9a 100644
--- a/interface/src/LODManager.cpp
+++ b/interface/src/LODManager.cpp
@@ -54,7 +54,9 @@ void LODManager::autoAdjustLOD(float batchTime, float engineRunTime, float delta
     float renderTime = batchTime + OVERLAY_AND_SWAP_TIME_BUDGET;
     float maxTime = glm::max(renderTime, engineRunTime);
     const float BLEND_TIMESCALE = 0.3f; // sec
-    float blend = BLEND_TIMESCALE / deltaTimeSec;
+    const float MIN_DELTA_TIME = 0.001f;
+    const float safeDeltaTime = glm::max(deltaTimeSec, MIN_DELTA_TIME);
+    float blend = BLEND_TIMESCALE / safeDeltaTime;
     if (blend > 1.0f) {
         blend = 1.0f;
     }
diff --git a/libraries/animation/src/Rig.cpp b/libraries/animation/src/Rig.cpp
index 3dad4e3fb6..f06156874b 100644
--- a/libraries/animation/src/Rig.cpp
+++ b/libraries/animation/src/Rig.cpp
@@ -39,7 +39,12 @@ static std::mutex rigRegistryMutex;
 
 static bool isEqual(const glm::vec3& u, const glm::vec3& v) {
     const float EPSILON = 0.0001f;
-    return glm::length(u - v) / glm::length(u) <= EPSILON;
+    float uLen = glm::length(u);
+    if (uLen == 0.0f) {
+        return glm::length(v) <= EPSILON;
+    } else {
+        return (glm::length(u - v) / uLen) <= EPSILON;
+    }
 }
 
 static bool isEqual(const glm::quat& p, const glm::quat& q) {
diff --git a/libraries/avatars-renderer/src/avatars-renderer/Avatar.cpp b/libraries/avatars-renderer/src/avatars-renderer/Avatar.cpp
index d2dc116e15..49d2431098 100644
--- a/libraries/avatars-renderer/src/avatars-renderer/Avatar.cpp
+++ b/libraries/avatars-renderer/src/avatars-renderer/Avatar.cpp
@@ -453,7 +453,9 @@ void Avatar::applyPositionDelta(const glm::vec3& delta) {
 void Avatar::measureMotionDerivatives(float deltaTime) {
     PerformanceTimer perfTimer("derivatives");
     // linear
-    float invDeltaTime = 1.0f / deltaTime;
+    const float MIN_DELTA_TIME = 0.001f;
+    const float safeDeltaTime = glm::max(deltaTime, MIN_DELTA_TIME);
+    float invDeltaTime = 1.0f / safeDeltaTime;
     // Floating point error prevents us from computing velocity in a naive way
     // (e.g. vel = (pos - oldPos) / dt) so instead we use _positionOffsetAccumulator.
     glm::vec3 velocity = _positionDeltaAccumulator * invDeltaTime;
diff --git a/libraries/shared/src/MovingMinMaxAvg.h b/libraries/shared/src/MovingMinMaxAvg.h
index 580baf7317..782b0dc523 100644
--- a/libraries/shared/src/MovingMinMaxAvg.h
+++ b/libraries/shared/src/MovingMinMaxAvg.h
@@ -59,8 +59,12 @@ public:
             _max = other._max;
         }
         double totalSamples = _samples + other._samples;
-        _average = _average * ((double)_samples / totalSamples)
-            + other._average * ((double)other._samples / totalSamples);
+        if (totalSamples > 0) {
+            _average = _average * ((double)_samples / totalSamples)
+                + other._average * ((double)other._samples / totalSamples);
+        } else {
+            _average = 0.0f;
+        }
         _samples += other._samples;
     }