diff --git a/src/Drawable.js b/src/Drawable.js
index 70c9928..5535b67 100644
--- a/src/Drawable.js
+++ b/src/Drawable.js
@@ -24,10 +24,10 @@ function Drawable(renderer, gl) {
      */
     this._uniforms = {
         /**
-         * The model-view-projection matrix.
+         * The model matrix, to concat with the projection matrix at draw time.
          * @type {module:twgl/m4.Mat4}
          */
-        u_mvp: twgl.m4.identity(),
+        u_modelMatrix: twgl.m4.identity(),
 
         /**
          * The nominal (not necessarily current) size of the current skin.
@@ -131,19 +131,6 @@ Drawable.getDrawableByID = function (drawableID) {
     return Drawable._allDrawables[drawableID];
 };
 
-/**
- * Dirty the transforms of all Drawables.
- * Call this when the projection matrix changes, for example.
- */
-Drawable.dirtyAllTransforms = function () {
-    for (var drawableID in Drawable._allDrawables) {
-        if (Drawable._allDrawables.hasOwnProperty(drawableID)) {
-            var drawable = Drawable._allDrawables[drawableID];
-            drawable.setTransformDirty();
-        }
-    }
-};
-
 // TODO: fall back on a built-in skin to protect against network problems
 Drawable._DEFAULT_SKIN = {
     squirrel: '7e24c99c1b853e52f8e7f9004416fa34.png',
@@ -403,18 +390,18 @@ Drawable.prototype._setSkinSize = function (width, height, costumeResolution) {
  * @private
  */
 Drawable.prototype._calculateTransform = function () {
-    var mvp = this._uniforms.u_mvp;
+    var modelMatrix = this._uniforms.u_modelMatrix;
 
-    var projection = this._renderer.getProjectionMatrix();
-    twgl.m4.translate(projection, this._position, mvp);
+    twgl.m4.identity(modelMatrix);
+    twgl.m4.translate(modelMatrix, this._position, modelMatrix);
 
     var rotation = (270 - this._direction) * Math.PI / 180;
-    twgl.m4.rotateZ(mvp, rotation, mvp);
+    twgl.m4.rotateZ(modelMatrix, rotation, modelMatrix);
 
     var scaledSize = twgl.v3.mulScalar(
         this._uniforms.u_skinSize, this._scale / 100);
     scaledSize[2] = 0; // was NaN because u_skinSize has only 2 components
-    twgl.m4.scale(mvp, scaledSize, mvp);
+    twgl.m4.scale(modelMatrix, scaledSize, modelMatrix);
 
     this._transformDirty = false;
 };
diff --git a/src/index.js b/src/index.js
index 2352ffe..7113196 100644
--- a/src/index.js
+++ b/src/index.js
@@ -79,7 +79,6 @@ RenderWebGL.prototype.setStageSize = function (xLeft, xRight, yBottom, yTop) {
     this._yBottom = yBottom;
     this._yTop = yTop;
     this._projection = twgl.m4.ortho(xLeft, xRight, yBottom, yTop, -1, 1);
-    Drawable.dirtyAllTransforms();
 };
 
 /**
@@ -118,9 +117,11 @@ RenderWebGL.prototype.draw = function () {
             currentShader = newShader;
             gl.useProgram(currentShader.program);
             twgl.setBuffersAndAttributes(gl, currentShader, this._bufferInfo);
+            twgl.setUniforms(
+                currentShader, {u_projectionMatrix: this._projection});
+            twgl.setUniforms(currentShader, {u_fudge: window.fudge || 0});
         }
         twgl.setUniforms(currentShader, drawable.getUniforms());
-        twgl.setUniforms(currentShader, {u_fudge: window.fudge || 0});
         twgl.drawBufferInfo(gl, gl.TRIANGLES, this._bufferInfo);
     }
 };
diff --git a/src/shaders/sprite.vert b/src/shaders/sprite.vert
index 03e074a..9eacc63 100644
--- a/src/shaders/sprite.vert
+++ b/src/shaders/sprite.vert
@@ -1,4 +1,5 @@
-uniform mat4 u_mvp;
+uniform mat4 u_projectionMatrix;
+uniform mat4 u_modelMatrix;
 
 attribute vec2 a_position;
 attribute vec2 a_texCoord;
@@ -6,6 +7,6 @@ attribute vec2 a_texCoord;
 varying vec2 v_texCoord;
 
 void main() {
-    gl_Position = u_mvp * vec4(a_position, 0, 1);
+    gl_Position = u_projectionMatrix * u_modelMatrix * vec4(a_position, 0, 1);
     v_texCoord = a_texCoord;
 }