diff --git a/piet-gpu-types/src/pathseg.rs b/piet-gpu-types/src/pathseg.rs
index 5ad382b..ab3fcd1 100644
--- a/piet-gpu-types/src/pathseg.rs
+++ b/piet-gpu-types/src/pathseg.rs
@@ -18,6 +18,25 @@ piet_gpu! {
             // halfwidth in both x and y for binning
             stroke: [f32; 2],
         }
+        struct PathFillCubic {
+            p0: [f32; 2],
+            p1: [f32; 2],
+            p2: [f32; 2],
+            p3: [f32; 2],
+            path_ix: u32,
+            // A note: the layout of this struct is shared with
+            // PathStrokeCubic. In that case, we actually write
+            // [0.0, 0.0] as the stroke field, to minimize divergence.
+        }
+        struct PathStrokeCubic {
+            p0: [f32; 2],
+            p1: [f32; 2],
+            p2: [f32; 2],
+            p3: [f32; 2],
+            path_ix: u32,
+            // halfwidth in both x and y for binning
+            stroke: [f32; 2],
+        }
         /*
         struct PathQuad {
             p0: [f32; 2],
@@ -37,6 +56,8 @@ piet_gpu! {
             Nop,
             FillLine(PathFillLine),
             StrokeLine(PathStrokeLine),
+            FillCubic(PathFillCubic),
+            StrokeCubic(PathStrokeCubic),
             /*
             Quad(AnnoQuadSeg),
             Cubic(AnnoCubicSeg),
diff --git a/piet-gpu-types/src/scene.rs b/piet-gpu-types/src/scene.rs
index 5792c94..5e4899f 100644
--- a/piet-gpu-types/src/scene.rs
+++ b/piet-gpu-types/src/scene.rs
@@ -92,10 +92,10 @@ piet_gpu! {
             StrokeLine(LineSeg),
             FillLine(LineSeg),
 
-            // Note: we'll need to handle the stroke/fill distinction
-            // for these as well, when we do flattening on the GPU.
-            Quad(QuadSeg),
-            Cubic(CubicSeg),
+            StrokeQuad(QuadSeg),
+            FillQuad(QuadSeg),
+            StrokeCubic(CubicSeg),
+            FillCubic(CubicSeg),
             Stroke(Stroke),
             Fill(Fill),
             SetLineWidth(SetLineWidth),
diff --git a/piet-gpu/shader/build.ninja b/piet-gpu/shader/build.ninja
index 4f6e07f..13fb1b2 100644
--- a/piet-gpu/shader/build.ninja
+++ b/piet-gpu/shader/build.ninja
@@ -16,7 +16,7 @@ build binning.spv: glsl binning.comp | annotated.h state.h bins.h setup.h
 
 build tile_alloc.spv: glsl tile_alloc.comp | annotated.h tile.h setup.h
 
-build path_coarse.spv: glsl path_coarse.comp | annotated.h tile.h setup.h
+build path_coarse.spv: glsl path_coarse.comp | annotated.h pathseg.h tile.h setup.h
 
 build backdrop.spv: glsl backdrop.comp | annotated.h tile.h setup.h
 
diff --git a/piet-gpu/shader/elements.comp b/piet-gpu/shader/elements.comp
index 230b710..0855219 100644
--- a/piet-gpu/shader/elements.comp
+++ b/piet-gpu/shader/elements.comp
@@ -115,14 +115,16 @@ State map_element(ElementRef ref, inout bool is_fill) {
         c.bbox.zw = max(line.p0, line.p1);
         c.pathseg_count = 1;
         break;
-    case Element_Quad:
-        QuadSeg quad = Element_Quad_read(ref);
+    case Element_FillQuad:
+    case Element_StrokeQuad:
+        QuadSeg quad = Element_FillQuad_read(ref);
         c.bbox.xy = min(min(quad.p0, quad.p1), quad.p2);
         c.bbox.zw = max(max(quad.p0, quad.p1), quad.p2);
         c.pathseg_count = 1;
         break;
-    case Element_Cubic:
-        CubicSeg cubic = Element_Cubic_read(ref);
+    case Element_FillCubic:
+    case Element_StrokeCubic:
+        CubicSeg cubic = Element_FillCubic_read(ref);
         c.bbox.xy = min(min(cubic.p0, cubic.p1), min(cubic.p2, cubic.p3));
         c.bbox.zw = max(max(cubic.p0, cubic.p1), max(cubic.p2, cubic.p3));
         c.pathseg_count = 1;
@@ -331,6 +333,27 @@ void main() {
             pathseg[path_out_ref.offset >> 2] = out_tag;
             PathStrokeLine_write(PathStrokeLineRef(path_out_ref.offset + 4), path_line);
             break;
+        case Element_FillCubic:
+        case Element_StrokeCubic:
+            CubicSeg cubic = Element_StrokeCubic_read(this_ref);
+            PathStrokeCubic path_cubic;
+            path_cubic.p0 = st.mat.xy * cubic.p0.x + st.mat.zw * cubic.p0.y + st.translate;
+            path_cubic.p1 = st.mat.xy * cubic.p1.x + st.mat.zw * cubic.p1.y + st.translate;
+            path_cubic.p1 = st.mat.xy * cubic.p2.x + st.mat.zw * cubic.p2.y + st.translate;
+            path_cubic.p1 = st.mat.xy * cubic.p3.x + st.mat.zw * cubic.p3.y + st.translate;
+            path_cubic.path_ix = st.path_count;
+            if (tag == Element_StrokeCubic) {
+                path_cubic.stroke = get_linewidth(st);
+            } else {
+                path_cubic.stroke = vec2(0.0);
+            }
+            // We do encoding a bit by hand to minimize divergence. Another approach
+            // would be to have a fill/stroke bool.
+            path_out_ref = PathSegRef((st.pathseg_count - 1) * PathSeg_size);
+            out_tag = tag == Element_FillLine ? PathSeg_FillCubic : PathSeg_StrokeCubic;
+            pathseg[path_out_ref.offset >> 2] = out_tag;
+            PathStrokeCubic_write(PathStrokeCubicRef(path_out_ref.offset + 4), path_cubic);
+            break;
         case Element_Stroke:
             Stroke stroke = Element_Stroke_read(this_ref);
             AnnoStroke anno_stroke;
diff --git a/piet-gpu/shader/elements.spv b/piet-gpu/shader/elements.spv
index 18f4dc5..55a43f2 100644
Binary files a/piet-gpu/shader/elements.spv and b/piet-gpu/shader/elements.spv differ
diff --git a/piet-gpu/shader/path_coarse.spv b/piet-gpu/shader/path_coarse.spv
index 8c61a4b..7098a63 100644
Binary files a/piet-gpu/shader/path_coarse.spv and b/piet-gpu/shader/path_coarse.spv differ
diff --git a/piet-gpu/shader/pathseg.h b/piet-gpu/shader/pathseg.h
index dc36d7e..de4ed28 100644
--- a/piet-gpu/shader/pathseg.h
+++ b/piet-gpu/shader/pathseg.h
@@ -8,6 +8,14 @@ struct PathStrokeLineRef {
     uint offset;
 };
 
+struct PathFillCubicRef {
+    uint offset;
+};
+
+struct PathStrokeCubicRef {
+    uint offset;
+};
+
 struct PathSegRef {
     uint offset;
 };
@@ -37,10 +45,41 @@ PathStrokeLineRef PathStrokeLine_index(PathStrokeLineRef ref, uint index) {
     return PathStrokeLineRef(ref.offset + index * PathStrokeLine_size);
 }
 
+struct PathFillCubic {
+    vec2 p0;
+    vec2 p1;
+    vec2 p2;
+    vec2 p3;
+    uint path_ix;
+};
+
+#define PathFillCubic_size 36
+
+PathFillCubicRef PathFillCubic_index(PathFillCubicRef ref, uint index) {
+    return PathFillCubicRef(ref.offset + index * PathFillCubic_size);
+}
+
+struct PathStrokeCubic {
+    vec2 p0;
+    vec2 p1;
+    vec2 p2;
+    vec2 p3;
+    uint path_ix;
+    vec2 stroke;
+};
+
+#define PathStrokeCubic_size 44
+
+PathStrokeCubicRef PathStrokeCubic_index(PathStrokeCubicRef ref, uint index) {
+    return PathStrokeCubicRef(ref.offset + index * PathStrokeCubic_size);
+}
+
 #define PathSeg_Nop 0
 #define PathSeg_FillLine 1
 #define PathSeg_StrokeLine 2
-#define PathSeg_size 32
+#define PathSeg_FillCubic 3
+#define PathSeg_StrokeCubic 4
+#define PathSeg_size 48
 
 PathSegRef PathSeg_index(PathSegRef ref, uint index) {
     return PathSegRef(ref.offset + index * PathSeg_size);
@@ -97,6 +136,77 @@ void PathStrokeLine_write(PathStrokeLineRef ref, PathStrokeLine s) {
     pathseg[ix + 6] = floatBitsToUint(s.stroke.y);
 }
 
+PathFillCubic PathFillCubic_read(PathFillCubicRef ref) {
+    uint ix = ref.offset >> 2;
+    uint raw0 = pathseg[ix + 0];
+    uint raw1 = pathseg[ix + 1];
+    uint raw2 = pathseg[ix + 2];
+    uint raw3 = pathseg[ix + 3];
+    uint raw4 = pathseg[ix + 4];
+    uint raw5 = pathseg[ix + 5];
+    uint raw6 = pathseg[ix + 6];
+    uint raw7 = pathseg[ix + 7];
+    uint raw8 = pathseg[ix + 8];
+    PathFillCubic s;
+    s.p0 = vec2(uintBitsToFloat(raw0), uintBitsToFloat(raw1));
+    s.p1 = vec2(uintBitsToFloat(raw2), uintBitsToFloat(raw3));
+    s.p2 = vec2(uintBitsToFloat(raw4), uintBitsToFloat(raw5));
+    s.p3 = vec2(uintBitsToFloat(raw6), uintBitsToFloat(raw7));
+    s.path_ix = raw8;
+    return s;
+}
+
+void PathFillCubic_write(PathFillCubicRef ref, PathFillCubic s) {
+    uint ix = ref.offset >> 2;
+    pathseg[ix + 0] = floatBitsToUint(s.p0.x);
+    pathseg[ix + 1] = floatBitsToUint(s.p0.y);
+    pathseg[ix + 2] = floatBitsToUint(s.p1.x);
+    pathseg[ix + 3] = floatBitsToUint(s.p1.y);
+    pathseg[ix + 4] = floatBitsToUint(s.p2.x);
+    pathseg[ix + 5] = floatBitsToUint(s.p2.y);
+    pathseg[ix + 6] = floatBitsToUint(s.p3.x);
+    pathseg[ix + 7] = floatBitsToUint(s.p3.y);
+    pathseg[ix + 8] = s.path_ix;
+}
+
+PathStrokeCubic PathStrokeCubic_read(PathStrokeCubicRef ref) {
+    uint ix = ref.offset >> 2;
+    uint raw0 = pathseg[ix + 0];
+    uint raw1 = pathseg[ix + 1];
+    uint raw2 = pathseg[ix + 2];
+    uint raw3 = pathseg[ix + 3];
+    uint raw4 = pathseg[ix + 4];
+    uint raw5 = pathseg[ix + 5];
+    uint raw6 = pathseg[ix + 6];
+    uint raw7 = pathseg[ix + 7];
+    uint raw8 = pathseg[ix + 8];
+    uint raw9 = pathseg[ix + 9];
+    uint raw10 = pathseg[ix + 10];
+    PathStrokeCubic s;
+    s.p0 = vec2(uintBitsToFloat(raw0), uintBitsToFloat(raw1));
+    s.p1 = vec2(uintBitsToFloat(raw2), uintBitsToFloat(raw3));
+    s.p2 = vec2(uintBitsToFloat(raw4), uintBitsToFloat(raw5));
+    s.p3 = vec2(uintBitsToFloat(raw6), uintBitsToFloat(raw7));
+    s.path_ix = raw8;
+    s.stroke = vec2(uintBitsToFloat(raw9), uintBitsToFloat(raw10));
+    return s;
+}
+
+void PathStrokeCubic_write(PathStrokeCubicRef ref, PathStrokeCubic s) {
+    uint ix = ref.offset >> 2;
+    pathseg[ix + 0] = floatBitsToUint(s.p0.x);
+    pathseg[ix + 1] = floatBitsToUint(s.p0.y);
+    pathseg[ix + 2] = floatBitsToUint(s.p1.x);
+    pathseg[ix + 3] = floatBitsToUint(s.p1.y);
+    pathseg[ix + 4] = floatBitsToUint(s.p2.x);
+    pathseg[ix + 5] = floatBitsToUint(s.p2.y);
+    pathseg[ix + 6] = floatBitsToUint(s.p3.x);
+    pathseg[ix + 7] = floatBitsToUint(s.p3.y);
+    pathseg[ix + 8] = s.path_ix;
+    pathseg[ix + 9] = floatBitsToUint(s.stroke.x);
+    pathseg[ix + 10] = floatBitsToUint(s.stroke.y);
+}
+
 uint PathSeg_tag(PathSegRef ref) {
     return pathseg[ref.offset >> 2];
 }
@@ -109,6 +219,14 @@ PathStrokeLine PathSeg_StrokeLine_read(PathSegRef ref) {
     return PathStrokeLine_read(PathStrokeLineRef(ref.offset + 4));
 }
 
+PathFillCubic PathSeg_FillCubic_read(PathSegRef ref) {
+    return PathFillCubic_read(PathFillCubicRef(ref.offset + 4));
+}
+
+PathStrokeCubic PathSeg_StrokeCubic_read(PathSegRef ref) {
+    return PathStrokeCubic_read(PathStrokeCubicRef(ref.offset + 4));
+}
+
 void PathSeg_Nop_write(PathSegRef ref) {
     pathseg[ref.offset >> 2] = PathSeg_Nop;
 }
@@ -123,3 +241,13 @@ void PathSeg_StrokeLine_write(PathSegRef ref, PathStrokeLine s) {
     PathStrokeLine_write(PathStrokeLineRef(ref.offset + 4), s);
 }
 
+void PathSeg_FillCubic_write(PathSegRef ref, PathFillCubic s) {
+    pathseg[ref.offset >> 2] = PathSeg_FillCubic;
+    PathFillCubic_write(PathFillCubicRef(ref.offset + 4), s);
+}
+
+void PathSeg_StrokeCubic_write(PathSegRef ref, PathStrokeCubic s) {
+    pathseg[ref.offset >> 2] = PathSeg_StrokeCubic;
+    PathStrokeCubic_write(PathStrokeCubicRef(ref.offset + 4), s);
+}
+
diff --git a/piet-gpu/shader/scene.h b/piet-gpu/shader/scene.h
index 5bb879b..3e57303 100644
--- a/piet-gpu/shader/scene.h
+++ b/piet-gpu/shader/scene.h
@@ -240,12 +240,14 @@ TransformRef Transform_index(TransformRef ref, uint index) {
 #define Element_Nop 0
 #define Element_StrokeLine 1
 #define Element_FillLine 2
-#define Element_Quad 3
-#define Element_Cubic 4
-#define Element_Stroke 5
-#define Element_Fill 6
-#define Element_SetLineWidth 7
-#define Element_Transform 8
+#define Element_StrokeQuad 3
+#define Element_FillQuad 4
+#define Element_StrokeCubic 5
+#define Element_FillCubic 6
+#define Element_Stroke 7
+#define Element_Fill 8
+#define Element_SetLineWidth 9
+#define Element_Transform 10
 #define Element_size 36
 
 ElementRef Element_index(ElementRef ref, uint index) {
@@ -455,11 +457,19 @@ LineSeg Element_FillLine_read(ElementRef ref) {
     return LineSeg_read(LineSegRef(ref.offset + 4));
 }
 
-QuadSeg Element_Quad_read(ElementRef ref) {
+QuadSeg Element_StrokeQuad_read(ElementRef ref) {
     return QuadSeg_read(QuadSegRef(ref.offset + 4));
 }
 
-CubicSeg Element_Cubic_read(ElementRef ref) {
+QuadSeg Element_FillQuad_read(ElementRef ref) {
+    return QuadSeg_read(QuadSegRef(ref.offset + 4));
+}
+
+CubicSeg Element_StrokeCubic_read(ElementRef ref) {
+    return CubicSeg_read(CubicSegRef(ref.offset + 4));
+}
+
+CubicSeg Element_FillCubic_read(ElementRef ref) {
     return CubicSeg_read(CubicSegRef(ref.offset + 4));
 }
 
diff --git a/piet-gpu/src/render_ctx.rs b/piet-gpu/src/render_ctx.rs
index 7908ff2..221b737 100644
--- a/piet-gpu/src/render_ctx.rs
+++ b/piet-gpu/src/render_ctx.rs
@@ -223,6 +223,24 @@ impl PietGpuRenderContext {
         self.pathseg_count += 1;
     }
 
+    fn encode_quad_seg(&mut self, seg: QuadSeg, is_fill: bool) {
+        if is_fill {
+            self.elements.push(Element::FillQuad(seg));
+        } else {
+            self.elements.push(Element::StrokeQuad(seg));
+        }
+        self.pathseg_count += 1;
+    }
+
+    fn encode_cubic_seg(&mut self, seg: CubicSeg, is_fill: bool) {
+        if is_fill {
+            self.elements.push(Element::FillCubic(seg));
+        } else {
+            self.elements.push(Element::StrokeCubic(seg));
+        }
+        self.pathseg_count += 1;
+    }
+
     fn encode_path(&mut self, path: impl Iterator<Item = PathEl>, is_fill: bool) {
         let flatten = true;
         if flatten {
@@ -286,7 +304,7 @@ impl PietGpuRenderContext {
                             p1: scene_p1,
                             p2: scene_p2,
                         };
-                        self.elements.push(Element::Quad(seg));
+                        self.encode_quad_seg(seg, is_fill);
                         last_pt = Some(scene_p2);
                     }
                     PathEl::CurveTo(p1, p2, p3) => {
@@ -299,7 +317,7 @@ impl PietGpuRenderContext {
                             p2: scene_p2,
                             p3: scene_p3,
                         };
-                        self.elements.push(Element::Cubic(seg));
+                        self.encode_cubic_seg(seg, is_fill);
                         last_pt = Some(scene_p3);
                     }
                     PathEl::ClosePath => {