diff --git a/piet-wgsl/shader/backdrop_dyn.wgsl b/piet-wgsl/shader/backdrop_dyn.wgsl
index e465677..085f44c 100644
--- a/piet-wgsl/shader/backdrop_dyn.wgsl
+++ b/piet-wgsl/shader/backdrop_dyn.wgsl
@@ -14,7 +14,7 @@ var<storage> paths: array<Path>;
 @group(0) @binding(2)
 var<storage, read_write> tiles: array<Tile>;
 
-const WG_SIZE = 256u;
+let WG_SIZE = 256u;
 
 var<workgroup> sh_row_width: array<u32, WG_SIZE>;
 var<workgroup> sh_row_count: array<u32, WG_SIZE>;
diff --git a/piet-wgsl/shader/binning.wgsl b/piet-wgsl/shader/binning.wgsl
index 1b8323b..900b6e0 100644
--- a/piet-wgsl/shader/binning.wgsl
+++ b/piet-wgsl/shader/binning.wgsl
@@ -38,15 +38,15 @@ struct BinHeader {
 var<storage, read_write> bin_header: array<BinHeader>;
 
 // conversion factors from coordinates to bin
-const SX = 0.00390625;
-const SY = 0.00390625;
+let SX = 0.00390625;
+let SY = 0.00390625;
 //let SX = 1.0 / f32(N_TILE_X * TILE_WIDTH);
 //let SY = 1.0 / f32(N_TILE_Y * TILE_HEIGHT);
 
-const WG_SIZE = 256u;
-const N_SLICE = 8u;
+let WG_SIZE = 256u;
+let N_SLICE = 8u;
 //const N_SLICE = WG_SIZE / 32u;
-const N_SUBSLICE = 4u;
+let N_SUBSLICE = 4u;
 
 var<workgroup> sh_bitmaps: array<array<atomic<u32>, N_TILE>, N_SLICE>;
 // store count values packed two u16's to a u32
@@ -62,7 +62,8 @@ fn main(
     for (var i = 0u; i < N_SLICE; i += 1u) {
         atomicStore(&sh_bitmaps[i][local_id.x], 0u);
     }
-
+    workgroupBarrier();
+    
     // Read inputs and determine coverage of bins
     let element_ix = global_id.x;
     var x0 = 0;
diff --git a/piet-wgsl/shader/clip_leaf.wgsl b/piet-wgsl/shader/clip_leaf.wgsl
index e12b869..6d922dd 100644
--- a/piet-wgsl/shader/clip_leaf.wgsl
+++ b/piet-wgsl/shader/clip_leaf.wgsl
@@ -26,7 +26,7 @@ var<storage, read_write> draw_monoids: array<DrawMonoid>;
 @group(0) @binding(6)
 var<storage, read_write> clip_bboxes: array<vec4<f32>>;
 
-const WG_SIZE = 256u;
+let WG_SIZE = 256u;
 var<workgroup> sh_bic: array<Bic, 510 >;
 var<workgroup> sh_stack: array<u32, WG_SIZE>;
 var<workgroup> sh_stack_bbox: array<vec4<f32>, WG_SIZE>;
diff --git a/piet-wgsl/shader/clip_reduce.wgsl b/piet-wgsl/shader/clip_reduce.wgsl
index cc2c8aa..935aea3 100644
--- a/piet-wgsl/shader/clip_reduce.wgsl
+++ b/piet-wgsl/shader/clip_reduce.wgsl
@@ -19,7 +19,7 @@ var<storage, read_write> reduced: array<Bic>;
 @group(0) @binding(4)
 var<storage, read_write> clip_out: array<ClipEl>;
 
-const WG_SIZE = 256u;
+let WG_SIZE = 256u;
 var<workgroup> sh_bic: array<Bic, WG_SIZE>;
 var<workgroup> sh_parent: array<u32, WG_SIZE>;
 var<workgroup> sh_path_ix: array<u32, WG_SIZE>;
diff --git a/piet-wgsl/shader/coarse.wgsl b/piet-wgsl/shader/coarse.wgsl
index 92596db..4e23a21 100644
--- a/piet-wgsl/shader/coarse.wgsl
+++ b/piet-wgsl/shader/coarse.wgsl
@@ -45,9 +45,9 @@ var<storage, read_write> ptcl: array<u32>;
 
 // Much of this code assumes WG_SIZE == N_TILE. If these diverge, then
 // a fair amount of fixup is needed.
-const WG_SIZE = 256u;
+let WG_SIZE = 256u;
 //const N_SLICE = WG_SIZE / 32u;
-const N_SLICE = 8u;
+let N_SLICE = 8u;
 
 var<workgroup> sh_bitmaps: array<array<atomic<u32>, N_TILE>, N_SLICE>;
 var<workgroup> sh_part_count: array<u32, WG_SIZE>;
diff --git a/piet-wgsl/shader/draw_leaf.wgsl b/piet-wgsl/shader/draw_leaf.wgsl
index a15ed0f..0c9a72d 100644
--- a/piet-wgsl/shader/draw_leaf.wgsl
+++ b/piet-wgsl/shader/draw_leaf.wgsl
@@ -28,7 +28,7 @@ var<storage, read_write> info: array<u32>;
 @group(0) @binding(6)
 var<storage, read_write> clip_inp: array<ClipInp>;
 
-const WG_SIZE = 256u;
+let WG_SIZE = 256u;
 
 // Possibly dedup?
 struct Transform {
diff --git a/piet-wgsl/shader/draw_reduce.wgsl b/piet-wgsl/shader/draw_reduce.wgsl
index efb3fb1..af17d78 100644
--- a/piet-wgsl/shader/draw_reduce.wgsl
+++ b/piet-wgsl/shader/draw_reduce.wgsl
@@ -12,7 +12,7 @@ var<storage> scene: array<u32>;
 @group(0) @binding(2)
 var<storage, read_write> reduced: array<DrawMonoid>;
 
-const WG_SIZE = 256u;
+let WG_SIZE = 256u;
 
 var<workgroup> sh_scratch: array<DrawMonoid, WG_SIZE>;
 
diff --git a/piet-wgsl/shader/fine.wgsl b/piet-wgsl/shader/fine.wgsl
index 5902b51..7b298ca 100644
--- a/piet-wgsl/shader/fine.wgsl
+++ b/piet-wgsl/shader/fine.wgsl
@@ -26,8 +26,8 @@ var<storage> segments: array<Segment>;
 #import blend
 #import ptcl
 
-const GRADIENT_WIDTH = 512;
-const BLEND_STACK_SPLIT = 4u;
+let GRADIENT_WIDTH = 512;
+let BLEND_STACK_SPLIT = 4u;
 
 @group(0) @binding(3)
 var output: texture_storage_2d<rgba8unorm, write>;
@@ -95,7 +95,7 @@ var output: texture_storage_2d<r8, write>;
 
 #endif
 
-const PIXELS_PER_THREAD = 4u;
+let PIXELS_PER_THREAD = 4u;
 
 fn fill_path(tile: Tile, xy: vec2<f32>) -> array<f32, PIXELS_PER_THREAD> {
     var area: array<f32, PIXELS_PER_THREAD>;
diff --git a/piet-wgsl/shader/path_coarse_full.wgsl b/piet-wgsl/shader/path_coarse_full.wgsl
index eafe3da..d6e5d91 100644
--- a/piet-wgsl/shader/path_coarse_full.wgsl
+++ b/piet-wgsl/shader/path_coarse_full.wgsl
@@ -45,12 +45,12 @@ struct SubdivResult {
     a2: f32,
 }
 
-const D = 0.67;
+let D = 0.67;
 fn approx_parabola_integral(x: f32) -> f32 {
     return x * inverseSqrt(sqrt(1.0 - D + (D * D * D * D + 0.25 * x * x)));
 }
 
-const B = 0.39;
+let B = 0.39;
 fn approx_parabola_inv_integral(x: f32) -> f32 {
     return x * sqrt(1.0 - B + (B * B + 0.5 * x * x));
 }
@@ -96,7 +96,7 @@ fn alloc_segment() -> u32 {
     return atomicAdd(&bump.segments, 1u) + 1u;
 }
 
-const MAX_QUADS = 16u;
+let MAX_QUADS = 16u;
 
 @compute @workgroup_size(256)
 fn main(
diff --git a/piet-wgsl/shader/pathtag_reduce.wgsl b/piet-wgsl/shader/pathtag_reduce.wgsl
index 80f9aed..3d00f4f 100644
--- a/piet-wgsl/shader/pathtag_reduce.wgsl
+++ b/piet-wgsl/shader/pathtag_reduce.wgsl
@@ -12,8 +12,8 @@ var<storage> scene: array<u32>;
 @group(0) @binding(2)
 var<storage, read_write> reduced: array<TagMonoid>;
 
-const LG_WG_SIZE = 8u;
-const WG_SIZE = 256u;
+let LG_WG_SIZE = 8u;
+let WG_SIZE = 256u;
 
 var<workgroup> sh_scratch: array<TagMonoid, WG_SIZE>;
 
diff --git a/piet-wgsl/shader/pathtag_scan.wgsl b/piet-wgsl/shader/pathtag_scan.wgsl
index 5e48f1d..f8a8005 100644
--- a/piet-wgsl/shader/pathtag_scan.wgsl
+++ b/piet-wgsl/shader/pathtag_scan.wgsl
@@ -15,8 +15,8 @@ var<storage> reduced: array<TagMonoid>;
 @group(0) @binding(3)
 var<storage, read_write> tag_monoids: array<TagMonoid>;
 
-const LG_WG_SIZE = 8u;
-const WG_SIZE = 256u;
+let LG_WG_SIZE = 8u;
+let WG_SIZE = 256u;
 
 var<workgroup> sh_parent: array<TagMonoid, WG_SIZE>;
 // These could be combined?
diff --git a/piet-wgsl/shader/shared/blend.wgsl b/piet-wgsl/shader/shared/blend.wgsl
index 27bbf6e..e101c70 100644
--- a/piet-wgsl/shader/shared/blend.wgsl
+++ b/piet-wgsl/shader/shared/blend.wgsl
@@ -2,23 +2,23 @@
 
 // Color mixing modes
 
-const MIX_NORMAL = 0u;
-const MIX_MULTIPLY = 1u;
-const MIX_SCREEN = 2u;
-const MIX_OVERLAY = 3u;
-const MIX_DARKEN = 4u;
-const MIX_LIGHTEN = 5u;
-const MIX_COLOR_DODGE = 6u;
-const MIX_COLOR_BURN = 7u;
-const MIX_HARD_LIGHT = 8u;
-const MIX_SOFT_LIGHT = 9u;
-const MIX_DIFFERENCE = 10u;
-const MIX_EXCLUSION = 11u;
-const MIX_HUE = 12u;
-const MIX_SATURATION = 13u;
-const MIX_COLOR = 14u;
-const MIX_LUMINOSITY = 15u;
-const MIX_CLIP = 128u;
+let MIX_NORMAL = 0u;
+let MIX_MULTIPLY = 1u;
+let MIX_SCREEN = 2u;
+let MIX_OVERLAY = 3u;
+let MIX_DARKEN = 4u;
+let MIX_LIGHTEN = 5u;
+let MIX_COLOR_DODGE = 6u;
+let MIX_COLOR_BURN = 7u;
+let MIX_HARD_LIGHT = 8u;
+let MIX_SOFT_LIGHT = 9u;
+let MIX_DIFFERENCE = 10u;
+let MIX_EXCLUSION = 11u;
+let MIX_HUE = 12u;
+let MIX_SATURATION = 13u;
+let MIX_COLOR = 14u;
+let MIX_LUMINOSITY = 15u;
+let MIX_CLIP = 128u;
 
 fn screen(cb: vec3<f32>, cs: vec3<f32>) -> vec3<f32> {
     return cb + cs - (cb * cs);
@@ -210,20 +210,20 @@ fn blend_mix(cb: vec3<f32>, cs: vec3<f32>, mode: u32) -> vec3<f32> {
 
 // Composition modes
 
-const COMPOSE_CLEAR = 0u;
-const COMPOSE_COPY = 1u;
-const COMPOSE_DEST = 2u;
-const COMPOSE_SRC_OVER = 3u;
-const COMPOSE_DEST_OVER = 4u;
-const COMPOSE_SRC_IN = 5u;
-const COMPOSE_DEST_IN = 6u;
-const COMPOSE_SRC_OUT = 7u;
-const COMPOSE_DEST_OUT = 8u;
-const COMPOSE_SRC_ATOP = 9u;
-const COMPOSE_DEST_ATOP = 10u;
-const COMPOSE_XOR = 11u;
-const COMPOSE_PLUS = 12u;
-const COMPOSE_PLUS_LIGHTER = 13u;
+let COMPOSE_CLEAR = 0u;
+let COMPOSE_COPY = 1u;
+let COMPOSE_DEST = 2u;
+let COMPOSE_SRC_OVER = 3u;
+let COMPOSE_DEST_OVER = 4u;
+let COMPOSE_SRC_IN = 5u;
+let COMPOSE_DEST_IN = 6u;
+let COMPOSE_SRC_OUT = 7u;
+let COMPOSE_DEST_OUT = 8u;
+let COMPOSE_SRC_ATOP = 9u;
+let COMPOSE_DEST_ATOP = 10u;
+let COMPOSE_XOR = 11u;
+let COMPOSE_PLUS = 12u;
+let COMPOSE_PLUS_LIGHTER = 13u;
 
 // Apply general compositing operation.
 // Inputs are separated colors and alpha, output is premultiplied.
diff --git a/piet-wgsl/shader/shared/config.wgsl b/piet-wgsl/shader/shared/config.wgsl
index 62b1160..29ea80b 100644
--- a/piet-wgsl/shader/shared/config.wgsl
+++ b/piet-wgsl/shader/shared/config.wgsl
@@ -29,10 +29,10 @@ struct Config {
 
 // Geometry of tiles and bins
 
-const TILE_WIDTH = 16u;
-const TILE_HEIGHT = 16u;
+let TILE_WIDTH = 16u;
+let TILE_HEIGHT = 16u;
 // Number of tiles per bin
-const N_TILE_X = 16u;
-const N_TILE_Y = 16u;
+let N_TILE_X = 16u;
+let N_TILE_Y = 16u;
 //const N_TILE = N_TILE_X * N_TILE_Y;
-const N_TILE = 256u;
+let N_TILE = 256u;
diff --git a/piet-wgsl/shader/shared/cubic.wgsl b/piet-wgsl/shader/shared/cubic.wgsl
index 5a5f4ae..72292a8 100644
--- a/piet-wgsl/shader/shared/cubic.wgsl
+++ b/piet-wgsl/shader/shared/cubic.wgsl
@@ -10,4 +10,4 @@ struct Cubic {
     flags: u32,
 }
 
-const CUBIC_IS_STROKE = 1u;
+let CUBIC_IS_STROKE = 1u;
diff --git a/piet-wgsl/shader/shared/drawtag.wgsl b/piet-wgsl/shader/shared/drawtag.wgsl
index 4dd604a..432cf1b 100644
--- a/piet-wgsl/shader/shared/drawtag.wgsl
+++ b/piet-wgsl/shader/shared/drawtag.wgsl
@@ -15,13 +15,13 @@ struct DrawMonoid {
 
 // Each draw object has a 32-bit draw tag, which is a bit-packed
 // version of the draw monoid.
-const DRAWTAG_NOP = 0u;
-const DRAWTAG_FILL_COLOR = 0x44u;
-const DRAWTAG_FILL_LIN_GRADIENT = 0x114u;
-const DRAWTAG_FILL_RAD_GRADIENT = 0x2dcu;
-const DRAWTAG_FILL_IMAGE = 0x48u;
-const DRAWTAG_BEGIN_CLIP = 0x9u;
-const DRAWTAG_END_CLIP = 0x21u;
+let DRAWTAG_NOP = 0u;
+let DRAWTAG_FILL_COLOR = 0x44u;
+let DRAWTAG_FILL_LIN_GRADIENT = 0x114u;
+let DRAWTAG_FILL_RAD_GRADIENT = 0x2dcu;
+let DRAWTAG_FILL_IMAGE = 0x48u;
+let DRAWTAG_BEGIN_CLIP = 0x9u;
+let DRAWTAG_END_CLIP = 0x21u;
 
 fn draw_monoid_identity() -> DrawMonoid {
     return DrawMonoid();
diff --git a/piet-wgsl/shader/shared/pathtag.wgsl b/piet-wgsl/shader/shared/pathtag.wgsl
index 03349fb..9777f47 100644
--- a/piet-wgsl/shader/shared/pathtag.wgsl
+++ b/piet-wgsl/shader/shared/pathtag.wgsl
@@ -11,15 +11,15 @@ struct TagMonoid {
 #endif
 }
 
-const PATH_TAG_SEG_TYPE = 3u;
-const PATH_TAG_LINETO = 1u;
-const PATH_TAG_QUADTO = 2u;
-const PATH_TAG_CUBICTO = 3u;
-const PATH_TAG_F32 = 8u;
-const PATH_TAG_TRANSFORM = 0x20u;
+let PATH_TAG_SEG_TYPE = 3u;
+let PATH_TAG_LINETO = 1u;
+let PATH_TAG_QUADTO = 2u;
+let PATH_TAG_CUBICTO = 3u;
+let PATH_TAG_F32 = 8u;
+let PATH_TAG_TRANSFORM = 0x20u;
 #ifdef full
-const PATH_TAG_PATH = 0x10u;
-const PATH_TAG_LINEWIDTH = 0x40u;
+let PATH_TAG_PATH = 0x10u;
+let PATH_TAG_LINEWIDTH = 0x40u;
 #endif
 
 fn tag_monoid_identity() -> TagMonoid {
diff --git a/piet-wgsl/shader/shared/ptcl.wgsl b/piet-wgsl/shader/shared/ptcl.wgsl
index 8df554a..3527bd0 100644
--- a/piet-wgsl/shader/shared/ptcl.wgsl
+++ b/piet-wgsl/shader/shared/ptcl.wgsl
@@ -2,23 +2,23 @@
 
 // Layout of per-tile command list
 // Initial allocation, in u32's.
-const PTCL_INITIAL_ALLOC = 64u;
-const PTCL_INCREMENT = 256u;
+let PTCL_INITIAL_ALLOC = 64u;
+let PTCL_INCREMENT = 256u;
 
 // Amount of space taken by jump
-const PTCL_HEADROOM = 2u;
+let PTCL_HEADROOM = 2u;
 
 // Tags for PTCL commands
-const CMD_END = 0u;
-const CMD_FILL = 1u;
-const CMD_STROKE = 2u;
-const CMD_SOLID = 3u;
-const CMD_COLOR = 5u;
-const CMD_LIN_GRAD = 6u;
-const CMD_RAD_GRAD = 7u;
-const CMD_BEGIN_CLIP = 9u;
-const CMD_END_CLIP = 10u;
-const CMD_JUMP = 11u;
+let CMD_END = 0u;
+let CMD_FILL = 1u;
+let CMD_STROKE = 2u;
+let CMD_SOLID = 3u;
+let CMD_COLOR = 5u;
+let CMD_LIN_GRAD = 6u;
+let CMD_RAD_GRAD = 7u;
+let CMD_BEGIN_CLIP = 9u;
+let CMD_END_CLIP = 10u;
+let CMD_JUMP = 11u;
 
 // The individual PTCL structs are written here, but read/write is by
 // hand in the relevant shaders
diff --git a/piet-wgsl/shader/tile_alloc.wgsl b/piet-wgsl/shader/tile_alloc.wgsl
index ad9e2f3..b7c6fd9 100644
--- a/piet-wgsl/shader/tile_alloc.wgsl
+++ b/piet-wgsl/shader/tile_alloc.wgsl
@@ -25,7 +25,7 @@ var<storage, read_write> paths: array<Path>;
 @group(0) @binding(5)
 var<storage, read_write> tiles: array<Tile>;
 
-const WG_SIZE = 256u;
+let WG_SIZE = 256u;
 
 var<workgroup> sh_tile_count: array<u32, WG_SIZE>;
 var<workgroup> sh_tile_offset: u32;
diff --git a/piet-wgsl/src/shaders/preprocess.rs b/piet-wgsl/src/shaders/preprocess.rs
index ac731c2..7bdb32a 100644
--- a/piet-wgsl/src/shaders/preprocess.rs
+++ b/piet-wgsl/src/shaders/preprocess.rs
@@ -140,7 +140,15 @@ pub fn preprocess(input: &str, defines: &HashSet<String>, imports: &HashMap<&str
             }
         }
         if stack.iter().all(|item| item.active) {
-            output.push_str(line);
+            // Naga does not yet recognize `const` but web does not allow global `let`. We
+            // use `let` in our canonical sources to satisfy wgsl-analyzer but replace with
+            // `const` when targeting web.
+            if cfg!(target_arch = "wasm32") && line.starts_with("let ") {
+                output.push_str("const");
+                output.push_str(&line[3..]);
+            } else {
+                output.push_str(line);
+            }
             output.push('\n');
         }
     }