diff --git a/assignment-client/src/avatars/AvatarMixerSlave.cpp b/assignment-client/src/avatars/AvatarMixerSlave.cpp
index f347ff1f10..c434d82116 100644
--- a/assignment-client/src/avatars/AvatarMixerSlave.cpp
+++ b/assignment-client/src/avatars/AvatarMixerSlave.cpp
@@ -329,6 +329,7 @@ void AvatarMixerSlave::broadcastAvatarDataToAgent(const SharedNodePointer& node)
             AvatarData::_avatarSortCoefficientSize,
             AvatarData::_avatarSortCoefficientCenter,
             AvatarData::_avatarSortCoefficientAge);
+    sortedAvatars.reserve(avatarsToSort.size());
 
     // ignore or sort
     const AvatarSharedPointer& thisAvatar = nodeData->getAvatarSharedPointer();
@@ -429,9 +430,9 @@ void AvatarMixerSlave::broadcastAvatarDataToAgent(const SharedNodePointer& node)
 
     int remainingAvatars = (int)sortedAvatars.size();
     auto traitsPacketList = NLPacketList::create(PacketType::BulkAvatarTraits, QByteArray(), true, true);
-    while (!sortedAvatars.empty()) {
-        const auto avatarData = sortedAvatars.top().getAvatar();
-        sortedAvatars.pop();
+    const auto& sortedAvatarVector = sortedAvatars.getSortedVector();
+    for (const auto& sortedAvatar : sortedAvatarVector) {
+        const auto& avatarData = sortedAvatar.getAvatar();
         remainingAvatars--;
 
         auto otherNode = avatarDataToNodes[avatarData];
diff --git a/interface/src/avatar/AvatarManager.cpp b/interface/src/avatar/AvatarManager.cpp
index 9a7d8ef0c8..e9486b9def 100644
--- a/interface/src/avatar/AvatarManager.cpp
+++ b/interface/src/avatar/AvatarManager.cpp
@@ -187,16 +187,17 @@ void AvatarManager::updateOtherAvatars(float deltaTime) {
         AvatarSharedPointer _avatar;
     };
 
+    auto avatarMap = getHashCopy();
+    AvatarHash::iterator itr = avatarMap.begin();
 
     const auto& views = qApp->getConicalViews();
     PrioritySortUtil::PriorityQueue<SortableAvatar> sortedAvatars(views,
             AvatarData::_avatarSortCoefficientSize,
             AvatarData::_avatarSortCoefficientCenter,
             AvatarData::_avatarSortCoefficientAge);
+    sortedAvatars.reserve(avatarMap.size() - 1); // don't include MyAvatar
 
     // sort
-    auto avatarMap = getHashCopy();
-    AvatarHash::iterator itr = avatarMap.begin();
     while (itr != avatarMap.end()) {
         const auto& avatar = std::static_pointer_cast<Avatar>(*itr);
         // DO NOT update _myAvatar!  Its update has already been done earlier in the main loop.
@@ -206,6 +207,7 @@ void AvatarManager::updateOtherAvatars(float deltaTime) {
         }
         ++itr;
     }
+    const auto& sortedAvatarVector = sortedAvatars.getSortedVector();
 
     // process in sorted order
     uint64_t startTime = usecTimestampNow();
@@ -216,8 +218,8 @@ void AvatarManager::updateOtherAvatars(float deltaTime) {
 
     render::Transaction renderTransaction;
     workload::Transaction workloadTransaction;
-    while (!sortedAvatars.empty()) {
-        const SortableAvatar& sortData = sortedAvatars.top();
+    for (auto it = sortedAvatarVector.begin(); it != sortedAvatarVector.end(); ++it) {
+        const SortableAvatar& sortData = *it;
         const auto avatar = std::static_pointer_cast<OtherAvatar>(sortData.getAvatar());
 
         // TODO: to help us scale to more avatars it would be nice to not have to poll orb state here
@@ -231,7 +233,6 @@ void AvatarManager::updateOtherAvatars(float deltaTime) {
 
         bool ignoring = DependencyManager::get<NodeList>()->isPersonalMutingNode(avatar->getID());
         if (ignoring) {
-            sortedAvatars.pop();
             continue;
         }
 
@@ -260,26 +261,19 @@ void AvatarManager::updateOtherAvatars(float deltaTime) {
             // --> some avatar velocity measurements may be a little off
 
             // no time to simulate, but we take the time to count how many were tragically missed
-            bool inView = sortData.getPriority() > OUT_OF_VIEW_THRESHOLD;
-            if (!inView) {
-                break;
-            }
-            if (inView && avatar->hasNewJointData()) {
-                numAVatarsNotUpdated++;
-            }
-            sortedAvatars.pop();
-            while (inView && !sortedAvatars.empty()) {
-                const SortableAvatar& newSortData = sortedAvatars.top();
+            while (it != sortedAvatarVector.end()) {
+                const SortableAvatar& newSortData = *it;
                 const auto newAvatar = std::static_pointer_cast<Avatar>(newSortData.getAvatar());
-                inView = newSortData.getPriority() > OUT_OF_VIEW_THRESHOLD;
-                if (inView && newAvatar->hasNewJointData()) {
-                    numAVatarsNotUpdated++;
+                bool inView = newSortData.getPriority() > OUT_OF_VIEW_THRESHOLD;
+                // Once we reach an avatar that's not in view, all avatars after it will also be out of view
+                if (!inView) {
+                    break;
                 }
-                sortedAvatars.pop();
+                numAVatarsNotUpdated += (int)(newAvatar->hasNewJointData());
+                ++it;
             }
             break;
         }
-        sortedAvatars.pop();
     }
 
     if (_shouldRender) {
diff --git a/interface/src/avatar/OtherAvatar.cpp b/interface/src/avatar/OtherAvatar.cpp
index 29ad5aed91..a0fa496c4c 100644
--- a/interface/src/avatar/OtherAvatar.cpp
+++ b/interface/src/avatar/OtherAvatar.cpp
@@ -29,20 +29,23 @@ OtherAvatar::~OtherAvatar() {
 }
 
 void OtherAvatar::removeOrb() {
-    if (qApp->getOverlays().isAddedOverlay(_otherAvatarOrbMeshPlaceholderID)) {
+    if (!_otherAvatarOrbMeshPlaceholderID.isNull()) {
         qApp->getOverlays().deleteOverlay(_otherAvatarOrbMeshPlaceholderID);
+        _otherAvatarOrbMeshPlaceholderID = UNKNOWN_OVERLAY_ID;
     }
 }
 
 void OtherAvatar::updateOrbPosition() {
     if (_otherAvatarOrbMeshPlaceholder != nullptr) {
         _otherAvatarOrbMeshPlaceholder->setWorldPosition(getHead()->getPosition());
+        if (_otherAvatarOrbMeshPlaceholderID.isNull()) {
+            _otherAvatarOrbMeshPlaceholderID = qApp->getOverlays().addOverlay(_otherAvatarOrbMeshPlaceholder);
+        }
     }
 }
 
 void OtherAvatar::createOrb() {
-    if (_otherAvatarOrbMeshPlaceholderID == UNKNOWN_OVERLAY_ID ||
-        !qApp->getOverlays().isAddedOverlay(_otherAvatarOrbMeshPlaceholderID)) {
+    if (_otherAvatarOrbMeshPlaceholderID.isNull()) {
         _otherAvatarOrbMeshPlaceholder = std::make_shared<Sphere3DOverlay>();
         _otherAvatarOrbMeshPlaceholder->setAlpha(1.0f);
         _otherAvatarOrbMeshPlaceholder->setColor({ 0xFF, 0x00, 0xFF });
diff --git a/libraries/controllers/src/controllers/UserInputMapper.cpp b/libraries/controllers/src/controllers/UserInputMapper.cpp
index 371deec7d5..307064c073 100755
--- a/libraries/controllers/src/controllers/UserInputMapper.cpp
+++ b/libraries/controllers/src/controllers/UserInputMapper.cpp
@@ -527,8 +527,8 @@ bool UserInputMapper::applyRoute(const Route::Pointer& route, bool force) {
     }
 
     // If the source hasn't been written yet, defer processing of this route
-    auto source = route->source;
-    auto sourceInput = source->getInput();
+    auto& source = route->source;
+    auto& sourceInput = source->getInput();
     if (sourceInput.device == STANDARD_DEVICE && !force && source->writeable()) {
         if (debugRoutes && route->debug) {
             qCDebug(controllers) << "Source not yet written, deferring";
@@ -559,7 +559,7 @@ bool UserInputMapper::applyRoute(const Route::Pointer& route, bool force) {
         return true;
     }
 
-    auto destination = route->destination;
+    auto& destination = route->destination;
     // THis could happen if the route destination failed to create
     // FIXME: Maybe do not create the route if the destination failed and avoid this case ?
     if (!destination) {
diff --git a/libraries/entities-renderer/src/EntityTreeRenderer.cpp b/libraries/entities-renderer/src/EntityTreeRenderer.cpp
index c3c4095251..3d782f69a7 100644
--- a/libraries/entities-renderer/src/EntityTreeRenderer.cpp
+++ b/libraries/entities-renderer/src/EntityTreeRenderer.cpp
@@ -382,6 +382,7 @@ void EntityTreeRenderer::updateChangedEntities(const render::ScenePointer& scene
 
         const auto& views = _viewState->getConicalViews();
         PrioritySortUtil::PriorityQueue<SortableRenderer> sortedRenderables(views);
+        sortedRenderables.reserve(_renderablesToUpdate.size());
         {
             PROFILE_RANGE_EX(simulation_physics, "SortRenderables", 0xffff00ff, (uint64_t)_renderablesToUpdate.size());
             std::unordered_map<EntityItemID, EntityRendererPointer>::iterator itr = _renderablesToUpdate.begin();
@@ -405,11 +406,14 @@ void EntityTreeRenderer::updateChangedEntities(const render::ScenePointer& scene
 
             // process the sorted renderables
             size_t numSorted = sortedRenderables.size();
-            while (!sortedRenderables.empty() && usecTimestampNow() < expiry) {
-                const auto renderable = sortedRenderables.top().getRenderer();
+            const auto& sortedRenderablesVector = sortedRenderables.getSortedVector();
+            for (const auto& sortedRenderable : sortedRenderablesVector) {
+                if (usecTimestampNow() > expiry) {
+                    break;
+                }
+                const auto& renderable = sortedRenderable.getRenderer();
                 renderable->updateInScene(scene, transaction);
                 _renderablesToUpdate.erase(renderable->getEntity()->getID());
-                sortedRenderables.pop();
             }
 
             // compute average per-renderable update cost
diff --git a/libraries/graphics/src/graphics/BufferViewHelpers.h b/libraries/graphics/src/graphics/BufferViewHelpers.h
index a9707c3128..026e7b53a3 100644
--- a/libraries/graphics/src/graphics/BufferViewHelpers.h
+++ b/libraries/graphics/src/graphics/BufferViewHelpers.h
@@ -13,6 +13,7 @@
 #include <glm/detail/type_vec.hpp>
 
 #include "GpuHelpers.h"
+#include "GLMHelpers.h"
 
 namespace graphics {
     class Mesh;
@@ -55,18 +56,16 @@ namespace buffer_helpers {
         tangent = glm::clamp(tangent, -1.0f, 1.0f);
         normal *= 511.0f;
         tangent *= 511.0f;
-        normal = glm::round(normal);
-        tangent = glm::round(tangent);
 
         glm::detail::i10i10i10i2 normalStruct;
         glm::detail::i10i10i10i2 tangentStruct;
-        normalStruct.data.x = int(normal.x);
-        normalStruct.data.y = int(normal.y);
-        normalStruct.data.z = int(normal.z);
+        normalStruct.data.x = fastLrintf(normal.x);
+        normalStruct.data.y = fastLrintf(normal.y);
+        normalStruct.data.z = fastLrintf(normal.z);
         normalStruct.data.w = 0;
-        tangentStruct.data.x = int(tangent.x);
-        tangentStruct.data.y = int(tangent.y);
-        tangentStruct.data.z = int(tangent.z);
+        tangentStruct.data.x = fastLrintf(tangent.x);
+        tangentStruct.data.y = fastLrintf(tangent.y);
+        tangentStruct.data.z = fastLrintf(tangent.z);
         tangentStruct.data.w = 0;
         packedNormal = normalStruct.pack;
         packedTangent = tangentStruct.pack;
diff --git a/libraries/shared/src/AABox.cpp b/libraries/shared/src/AABox.cpp
index b4384c494f..ff6c2a4e6e 100644
--- a/libraries/shared/src/AABox.cpp
+++ b/libraries/shared/src/AABox.cpp
@@ -79,33 +79,43 @@ void AABox::setBox(const glm::vec3& corner, const glm::vec3& scale) {
 
 glm::vec3 AABox::getFarthestVertex(const glm::vec3& normal) const {
     glm::vec3 result = _corner;
-    if (normal.x > 0.0f) {
-        result.x += _scale.x;
-    }
-    if (normal.y > 0.0f) {
-        result.y += _scale.y;
-    }
-    if (normal.z > 0.0f) {
-        result.z += _scale.z;
-    }
+    // This is a branchless version of:
+    //if (normal.x > 0.0f) {
+    //    result.x += _scale.x;
+    //}
+    //if (normal.y > 0.0f) {
+    //    result.y += _scale.y;
+    //}
+    //if (normal.z > 0.0f) {
+    //    result.z += _scale.z;
+    //}
+    float blend = (float)(normal.x > 0.0f);
+    result.x += blend * _scale.x + (1.0f - blend) * 0.0f;
+    blend = (float)(normal.y > 0.0f);
+    result.y += blend * _scale.y + (1.0f - blend) * 0.0f;
+    blend = (float)(normal.z > 0.0f);
+    result.z += blend * _scale.z + (1.0f - blend) * 0.0f;
     return result;
 }
 
 glm::vec3 AABox::getNearestVertex(const glm::vec3& normal) const {
     glm::vec3 result = _corner;
-
-    if (normal.x < 0.0f) {
-        result.x += _scale.x;
-    }
-
-    if (normal.y < 0.0f) {
-        result.y += _scale.y;
-    }
-
-    if (normal.z < 0.0f) {
-        result.z += _scale.z;
-    }
-
+    // This is a branchless version of:
+    //if (normal.x < 0.0f) {
+    //    result.x += _scale.x;
+    //}
+    //if (normal.y < 0.0f) {
+    //    result.y += _scale.y;
+    //}
+    //if (normal.z < 0.0f) {
+    //    result.z += _scale.z;
+    //}
+    float blend = (float)(normal.x < 0.0f);
+    result.x += blend * _scale.x + (1.0f - blend) * 0.0f;
+    blend = (float)(normal.y < 0.0f);
+    result.y += blend * _scale.y + (1.0f - blend) * 0.0f;
+    blend = (float)(normal.z < 0.0f);
+    result.z += blend * _scale.z + (1.0f - blend) * 0.0f;
     return result;
 }
 
@@ -459,28 +469,6 @@ AABox AABox::clamp(float min, float max) const {
     return AABox(clampedCorner, clampedScale);
 }
 
-AABox& AABox::operator += (const glm::vec3& point) {
-
-    if (isInvalid()) {
-        _corner = glm::min(_corner, point);
-    } else {
-        glm::vec3 maximum(_corner + _scale);
-        _corner = glm::min(_corner, point);
-        maximum = glm::max(maximum, point);
-        _scale = maximum - _corner;
-    }
-
-    return (*this);
-}
-
-AABox& AABox::operator += (const AABox& box) {
-    if (!box.isInvalid()) {
-        (*this) += box._corner;
-        (*this) += box.calcTopFarLeft();
-    }
-    return (*this);
-}
-
 void AABox::embiggen(float scale) {
     _corner += scale * (-0.5f * _scale);
     _scale *= scale;
diff --git a/libraries/shared/src/AABox.h b/libraries/shared/src/AABox.h
index daad01d7c7..f41bb8a814 100644
--- a/libraries/shared/src/AABox.h
+++ b/libraries/shared/src/AABox.h
@@ -85,8 +85,23 @@ public:
     AABox clamp(const glm::vec3& min, const glm::vec3& max) const;
     AABox clamp(float min, float max) const;
 
-    AABox& operator += (const glm::vec3& point);
-    AABox& operator += (const AABox& box);
+    inline AABox& operator+=(const glm::vec3& point) {
+        bool valid = !isInvalid();
+        glm::vec3 maximum = glm::max(_corner + _scale, point);
+        _corner = glm::min(_corner, point);
+        if (valid) {
+            _scale = maximum - _corner;
+        }
+        return (*this);
+    }
+
+    inline AABox& operator+=(const AABox& box) {
+        if (!box.isInvalid()) {
+            (*this) += box._corner;
+            (*this) += box.calcTopFarLeft();
+        }
+        return (*this);
+    }
 
     // Translate the AABox just moving the corner
     void translate(const glm::vec3& translation) { _corner += translation; }
@@ -114,7 +129,7 @@ public:
 
     static const glm::vec3 INFINITY_VECTOR;
 
-    bool isInvalid() const { return _corner == INFINITY_VECTOR; }
+    bool isInvalid() const { return _corner.x == std::numeric_limits<float>::infinity(); }
 
     void clear() { _corner = INFINITY_VECTOR; _scale = glm::vec3(0.0f); }
 
diff --git a/libraries/shared/src/GLMHelpers.h b/libraries/shared/src/GLMHelpers.h
index 7e6ef4cb28..96219ea48c 100644
--- a/libraries/shared/src/GLMHelpers.h
+++ b/libraries/shared/src/GLMHelpers.h
@@ -316,4 +316,17 @@ inline void glm_mat4u_mul(const glm::mat4& m1, const glm::mat4& m2, glm::mat4& r
 #endif
 }
 
+// convert float to int, using round-to-nearest-even (undefined on overflow)
+inline int fastLrintf(float x) {
+#if GLM_ARCH & GLM_ARCH_SSE2_BIT
+    return _mm_cvt_ss2si(_mm_set_ss(x));
+#else
+    // return lrintf(x);
+    static_assert(std::numeric_limits<double>::is_iec559, "Requires IEEE-754 double precision format");
+    union { double d; int64_t i; } bits = { (double)x };
+    bits.d += (3ULL << 51);
+    return (int)bits.i;
+#endif
+}
+
 #endif // hifi_GLMHelpers_h
diff --git a/libraries/shared/src/PrioritySortUtil.h b/libraries/shared/src/PrioritySortUtil.h
index 34ec074d45..8ded047212 100644
--- a/libraries/shared/src/PrioritySortUtil.h
+++ b/libraries/shared/src/PrioritySortUtil.h
@@ -12,7 +12,6 @@
 #define hifi_PrioritySortUtil_h
 
 #include <glm/glm.hpp>
-#include <queue>
 
 #include "NumericalConstants.h"
 #include "shared/ConicalViewFrustum.h"
@@ -75,7 +74,6 @@ namespace PrioritySortUtil {
 
         void setPriority(float priority) { _priority = priority; }
         float getPriority() const { return _priority; }
-        bool operator<(const Sortable& other) const { return _priority < other._priority; }
     private:
         float _priority { 0.0f };
     };
@@ -97,14 +95,18 @@ namespace PrioritySortUtil {
             _ageWeight = ageWeight;
         }
 
-        size_t size() const { return _queue.size(); }
+        size_t size() const { return _vector.size(); }
         void push(T thing) {
             thing.setPriority(computePriority(thing));
-            _queue.push(thing);
+            _vector.push_back(thing);
+        }
+        void reserve(size_t num) {
+            _vector.reserve(num);
+        }
+        const std::vector<T>& getSortedVector() {
+            std::sort(_vector.begin(), _vector.end(), [](const T& left, const T& right) { return left.getPriority() > right.getPriority(); });
+            return _vector;
         }
-        const T& top() const { return _queue.top(); }
-        void pop() { return _queue.pop(); }
-        bool empty() const { return _queue.empty(); }
 
     private:
 
@@ -153,7 +155,7 @@ namespace PrioritySortUtil {
         }
 
         ConicalViewFrustums _views;
-        std::priority_queue<T> _queue;
+        std::vector<T> _vector;
         float _angularWeight { DEFAULT_ANGULAR_COEF };
         float _centerWeight { DEFAULT_CENTER_COEF };
         float _ageWeight { DEFAULT_AGE_COEF };
diff --git a/tests/shared/src/AACubeTests.cpp b/tests/shared/src/AACubeTests.cpp
index 95a4d7f9f0..4ed3ee2813 100644
--- a/tests/shared/src/AACubeTests.cpp
+++ b/tests/shared/src/AACubeTests.cpp
@@ -168,12 +168,13 @@ void AACubeTests::rayVsParabolaPerformance() {
 
     glm::vec3 origin(0.0f);
     glm::vec3 direction = glm::normalize(glm::vec3(1.0f));
+    glm::vec3 invDirection = 1.0f / direction;
     float distance;
     BoxFace face;
     glm::vec3 normal;
     auto start = std::chrono::high_resolution_clock::now();
     for (auto& cube : cubes) {
-        if (cube.findRayIntersection(origin, direction, distance, face, normal)) {
+        if (cube.findRayIntersection(origin, direction, invDirection, distance, face, normal)) {
             numRayHits++;
         }
     }
diff --git a/tests/shared/src/GLMHelpersTests.cpp b/tests/shared/src/GLMHelpersTests.cpp
index 93c4735a6d..71877e89f6 100644
--- a/tests/shared/src/GLMHelpersTests.cpp
+++ b/tests/shared/src/GLMHelpersTests.cpp
@@ -214,3 +214,39 @@ void GLMHelpersTests::testGenerateBasisVectors() {
         QCOMPARE_WITH_ABS_ERROR(w, z, EPSILON);
     }
 }
+
+void GLMHelpersTests::roundPerf() {
+    const int NUM_VECS = 1000000;
+    const float MAX_VEC = 500.0f;
+    std::vector<glm::vec3> vecs;
+    vecs.reserve(NUM_VECS);
+    for (int i = 0; i < NUM_VECS; i++) {
+        vecs.emplace_back(randFloatInRange(-MAX_VEC, MAX_VEC), randFloatInRange(-MAX_VEC, MAX_VEC), randFloatInRange(-MAX_VEC, MAX_VEC));
+    }
+    std::vector<glm::vec3> vecs2 = vecs;
+    std::vector<glm::vec3> originalVecs = vecs;
+
+    auto start = std::chrono::high_resolution_clock::now();
+    for (auto& vec : vecs) {
+        vec = glm::round(vec);
+    }
+
+    auto glmTime = std::chrono::high_resolution_clock::now() - start;
+    start = std::chrono::high_resolution_clock::now();
+    for (auto& vec : vecs2) {
+        vec = glm::vec3(fastLrintf(vec.x), fastLrintf(vec.y), fastLrintf(vec.z));
+    }
+    auto manualTime = std::chrono::high_resolution_clock::now() - start;
+
+    bool identical = true;
+    for (int i = 0; i < vecs.size(); i++) {
+        identical &= vecs[i] == vecs2[i];
+        if (vecs[i] != vecs2[i]) {
+            qDebug() << "glm: " << vecs[i].x << vecs[i].y << vecs[i].z << ", manual: " << vecs2[i].x << vecs2[i].y << vecs2[i].z;
+            qDebug() << "original: " << originalVecs[i].x << originalVecs[i].y << originalVecs[i].z;
+            break;
+        }
+    }
+
+    qDebug() << "ratio: " << (float)glmTime.count() / (float)manualTime.count() << ", identical: " << identical;
+}
\ No newline at end of file
diff --git a/tests/shared/src/GLMHelpersTests.h b/tests/shared/src/GLMHelpersTests.h
index 030f2d477f..4d9bd0bb60 100644
--- a/tests/shared/src/GLMHelpersTests.h
+++ b/tests/shared/src/GLMHelpersTests.h
@@ -22,6 +22,7 @@ private slots:
     void testSixByteOrientationCompression();
     void testSimd();
     void testGenerateBasisVectors();
+    void roundPerf();
 };
 
 float getErrorDifference(const float& a, const float& b);