diff --git a/src/circuit/KetShaderUtil.js b/src/circuit/KetShaderUtil.js
index 882e2d60..0bf27955 100644
--- a/src/circuit/KetShaderUtil.js
+++ b/src/circuit/KetShaderUtil.js
@@ -86,20 +86,31 @@ const ketShaderPermute = (head, body, span=null) => ketShader(
     span);
 
 /**
- * @param {!String} head
- * @param {!String} body
- * @param {null|!int=null} span
+ * Returns a shader that multiplies each of the amplitudes in a superposition by computed phase factors.
+ *
+ * @param {!String} head Header code defining shader methods, uniforms, etc.
+ * @param {!String} body The body of a shader method returning the number of radians to phase by.
+ * @param {null|!int=null} span The number of qubits this operation applies to, if known ahead of time.
  * @return {!{withArgs: !function(args: ...!WglArg) : !WglConfiguredShader}}
  */
 const ketShaderPhase = (head, body, span=null) => ketShader(
-    head + `vec2 _ketgen_phase_for(float out_id) { ${body} }`,
-    'return cmul(amp, _ketgen_phase_for(out_id));',
+    `${head}
+        float _ketgen_phase_for(float out_id) {
+            ${body}
+        }
+    `,
+    `
+        float angle = _ketgen_phase_for(out_id);
+        return cmul(amp, vec2(cos(angle), sin(angle)));
+    `,
     span);
 
 /**
- * @param {!CircuitEvalContext} ctx
- * @param {undefined|!int=undefined} span
- * @param {undefined|!Array.<!string>} input_letters
+ * Determines some arguments to give to a shader produced by one of the ketShader methods.
+ *
+ * @param {!CircuitEvalContext} ctx The context in which the ket shader is being applied.
+ * @param {undefined|!int=undefined} span The number of qubits this shader applies to (if wasn't known ahead of time).
+ * @param {undefined|!Array.<!string>} input_letters The input gates that this shader cares about.
  * @returns {!Array.<!WglArg>}
  */
 function ketArgs(ctx, span=undefined, input_letters=[]) {
diff --git a/src/gates/FourierTransformGates.js b/src/gates/FourierTransformGates.js
index 3f3182b3..c7d36088 100644
--- a/src/gates/FourierTransformGates.js
+++ b/src/gates/FourierTransformGates.js
@@ -35,8 +35,7 @@ const CONTROLLED_PHASE_GRADIENT_SHADER = ketShaderPhase(
     `
         float hold = floor(out_id * 2.0 / span);
         float step = mod(out_id, span / 2.0);
-        float angle = hold * step * factor * 6.2831853071795864769 / span;
-        return vec2(cos(angle), sin(angle));
+        return hold * step * factor * 6.2831853071795864769 / span;
     `);
 
 const FOURIER_TRANSFORM_MATRIX_MAKER = span =>
diff --git a/src/gates/ParametrizedRotationGates.js b/src/gates/ParametrizedRotationGates.js
index 4f4b2e1d..fabfa6b3 100644
--- a/src/gates/ParametrizedRotationGates.js
+++ b/src/gates/ParametrizedRotationGates.js
@@ -71,8 +71,7 @@ const Z_TO_A_SHADER = ketShaderPhase(
         ${ketInputGateShaderCode('A')}
     `,
     `
-        float angle = read_input_A() * out_id * factor / _gen_input_span_A;
-        return vec2(cos(angle), sin(angle));
+        return read_input_A() * out_id * factor / _gen_input_span_A;
     `);
 
 ParametrizedRotationGates.XToA = new GateBuilder().
diff --git a/src/gates/PhaseGradientGates.js b/src/gates/PhaseGradientGates.js
index 6c1a674e..80abfc1f 100644
--- a/src/gates/PhaseGradientGates.js
+++ b/src/gates/PhaseGradientGates.js
@@ -37,8 +37,7 @@ const PHASE_GRADIENT_SHADER = ketShaderPhase(
         }
     `,
     `
-        float angle = angle_mul(factor, out_id);
-        return vec2(cos(angle), sin(angle));
+        return angle_mul(factor, out_id);
     `);
 
 let PhaseGradientGates = {};
diff --git a/test/circuit/KetShaderUtil.test.js b/test/circuit/KetShaderUtil.test.js
index 25dda0ba..5f222ee4 100644
--- a/test/circuit/KetShaderUtil.test.js
+++ b/test/circuit/KetShaderUtil.test.js
@@ -49,7 +49,7 @@ suite.testUsingWebGL("ketShaderPermute", () => {
 suite.testUsingWebGL("ketShaderPhase", () => {
     let shader = ketShaderPhase(
         '',
-        'return vec2(cos(out_id/10.0), sin(out_id/10.0));',
+        'return out_id/10.0;',
         3);
     assertThatCircuitShaderActsLikeMatrix(
         ctx => shader.withArgs(...ketArgs(ctx)),