diff --git a/docs/context-2d.md b/docs/context-2d.md
index 3c0b448..6bde946 100644
--- a/docs/context-2d.md
+++ b/docs/context-2d.md
@@ -725,6 +725,45 @@ whose shadow can land on the target at all (its own bounds, moved back by
 the offset and grown by the blur's reach), so a shape mostly off-screen does
 not allocate a surface the size of its bounding box.
 
+### How strong a shadow gets, and how to test one
+
+A blurred shadow reaches `shadowColor` only where the shape casting it is
+wide compared with the blur. That follows from what a blur *is* — coverage
+convolved with a gaussian — but it surprises people looking at pixels, so
+here it is in numbers, with σ = `shadowBlur / 2`:
+
+| what casts it | `shadowBlur` | peak alpha |
+| --- | --- | --- |
+| a 60×40 rect | 30 (σ 15) | 0.78 |
+| a 60×40 rect | 8 (σ 4) | 1.00 |
+| 48px glyph stems | 14 (σ 7) | 0.37 |
+
+A glyph stem five pixels wide against σ 7 keeps about `erf(5 / (2√2 · 7))`
+of its coverage — under a third — and that is what a browser draws too. So
+**an exact-colour pixel assertion is the wrong test for a shadow**: a
+"count the pixels within 90 of `#ff0000`" check finds nothing on a canvas
+whose red glyph shadow is plainly visible, because no pixel on it is ever
+that red (issue #287).
+
+What to assert instead:
+
+- **the shadow's own alpha**, on a transparent target. Draw with
+  `fillStyle = 'rgba(0, 0, 0, 0)'` so only the shadow paints, and read the
+  alpha channel out of `getImageData` — it is the coverage, with no
+  background mixed into it
+- **a difference between two places**, rather than a colour: darker (or
+  more tinted) where the shadow is than where it is not, at an offset the
+  drawing itself does not reach
+- **the profile**, when the blur itself is what is under test: a blurred
+  straight edge follows the gaussian's CDF, so coverage at ±σ is
+  0.841 / 0.159 (this is what `test/shadow.test.js` and
+  `test/smoke-canvas.test.js` check)
+
+None of this changes with the server. Shadows render identically on
+node-x11's in-process JS X server and on Xorg — same requests, same
+pixels — and both suites pin the same numbers; see
+[xserver.md](xserver.md).
+
 ## Text
 
 Text is fully shaped: OpenType kerning and ligatures, contextual forms for
diff --git a/docs/xserver.md b/docs/xserver.md
index 470d0ec..8d8b307 100644
--- a/docs/xserver.md
+++ b/docs/xserver.md
@@ -35,3 +35,10 @@ Rasterization is antialiased but intentionally not pixel-exact with Xorg —
 assert on regions/tolerances, not exact edge pixels (see
 `test/xserver.test.js` for the patterns; that suite runs ntk end-to-end
 against this server with no `$DISPLAY` and no fontconfig).
+
+Server-side *filtering* is exact, though, and shadows are the case worth
+naming: the `convolution` filter behind `shadowBlur` produces the same
+pixels here as on Xorg, so a shadow that seems to vanish under a headless
+harness is an assertion problem rather than a missing request (issue #287).
+[context-2d.md](context-2d.md#how-strong-a-shadow-gets-and-how-to-test-one)
+has the numbers and what to assert.
diff --git a/test/shadow.test.js b/test/shadow.test.js
index 666afb3..735e0ed 100644
--- a/test/shadow.test.js
+++ b/test/shadow.test.js
@@ -506,3 +506,64 @@ describe('shadows on laid-out text', () => {
     ctx.destroy();
   });
 });
+
+// ------------------------------------------------------------------
+// how strong a blurred shadow gets (issue #287)
+
+describe('how strong a blurred shadow gets', () => {
+  // Issue #287 read a shadow as missing on this very server because nothing
+  // on the canvas came within a tolerance of `shadowColor` itself. Nothing
+  // was missing: a blurred shadow only *reaches* its colour where the shape
+  // casting it is wide compared with the blur, and a glyph stem never is.
+  // The numbers below are the ones that decided it, and they are the same on
+  // Xorg (test/smoke-canvas.test.js pins the rect case there too).
+
+  /** the shadow's own alpha, straight from getImageData, over the surface */
+  const shadowAlpha = async (ctx, w, h) => {
+    const img = await ctx.getImageData(0, 0, w, h);
+    let peak = 0;
+    let painted = 0;
+    for (let i = 3; i < img.data.length; i += 4) {
+      if (img.data[i] > 0) painted++;
+      if (img.data[i] > peak) peak = img.data[i];
+    }
+    return { peak, painted };
+  };
+
+  test('a shape much wider than the blur reaches the shadow colour', async () => {
+    const w = 180;
+    const h = 140;
+    const ctx = target(w, h);
+    ctx.shadowColor = '#ff0000';
+    ctx.shadowBlur = 30; // sigma 15, so a 60x40 rect is 4 sigma by 2.7
+    ctx.fillStyle = 'rgba(0, 0, 0, 0)'; // only the shadow paints
+    ctx.fillRect(60, 50, 60, 40);
+    const { peak } = await shadowAlpha(ctx, w, h);
+    // convolving that rect with the same kernel gives 0.784 of full alpha —
+    // the interior is not opaque either, because 60x40 is not wide enough
+    // for one, and the gaussian says exactly how much it keeps
+    assert.ok(Math.abs(peak - 200) <= 4, `the middle of the shadow is ${peak}, expected ~200`);
+    ctx.destroy();
+  });
+
+  test('the shadow of 48px glyphs peaks at about a third of it', async () => {
+    const w = 200;
+    const h = 120;
+    const ctx = target(w, h);
+    ctx.font = '48px sans-serif';
+    ctx.shadowColor = '#ff0000';
+    ctx.shadowBlur = 14;
+    ctx.shadowOffsetX = 5;
+    ctx.shadowOffsetY = 5;
+    ctx.fillStyle = 'rgba(0, 0, 0, 0)';
+    ctx.fillText('AAA', 10, 70);
+    const { peak, painted } = await shadowAlpha(ctx, w, h);
+    assert.ok(painted > 2000, `the shadow is there (${painted} painted pixels)`);
+    // a 48px stem is about 5px wide against sigma 7: erf(5 / (2*sqrt(2)*7))
+    // is 0.28, and two neighbouring stems add to a little over a third
+    assert.ok(peak > 60 && peak < 140, `peak alpha ${peak}, expected ~94`);
+    // which is why a test that looks for `shadowColor` itself finds nothing
+    assert.ok(peak < 165, 'nothing on the canvas is within 90 of the colour');
+    ctx.destroy();
+  });
+});
diff --git a/test/smoke-canvas.test.js b/test/smoke-canvas.test.js
index 77a4176..535e8de 100644
--- a/test/smoke-canvas.test.js
+++ b/test/smoke-canvas.test.js
@@ -370,3 +370,29 @@ test('shadows: offset, blurred and coloured, on a real server', async (t) => {
   blurred.pixmap.destroy();
   pixmap.destroy();
 });
+
+test('shadows: a wide blur keeps the same fraction of its colour here (#287)', async (t) => {
+  if (skip) return t.skip(skip);
+  // The one number issue #287 turned on: how *strong* a blurred shadow gets.
+  // A shadow only reaches `shadowColor` where the shape casting it is wide
+  // compared with the blur, so the interior of a 60x40 rect at sigma 15 is
+  // 0.784 of full alpha and not 1 — and reading that as "the shadow is
+  // missing" is what the issue did. The hermetic run asserts the same 0.784
+  // against node-x11's JS server (test/shadow.test.js); this asserts Xorg
+  // agrees, which is the claim the issue needed and nothing was checking.
+  const { pixmap, ctx } = freshCtx(180);
+
+  ctx.shadowColor = 'black';
+  ctx.shadowBlur = 30;
+  ctx.fillStyle = 'rgba(0, 0, 0, 0)'; // only the shadow paints
+  ctx.fillRect(60, 50, 60, 40);
+
+  const image = await readPixels(ctx, 180, 180);
+  // black shadow on white: alpha is 1 - grey
+  const alpha = 1 - px(image, 180, 90, 70)[0] / 255;
+  assert.ok(
+    Math.abs(alpha - 0.784) < 0.03,
+    `the middle of the shadow is ${alpha.toFixed(3)} of the colour, expected ~0.784`
+  );
+  pixmap.destroy();
+});