diff --git a/src/lib/readme.test.ts b/src/lib/readme.test.ts
index c653dfb..9308c8c 100644
--- a/src/lib/readme.test.ts
+++ b/src/lib/readme.test.ts
@@ -71,6 +71,14 @@ describe("parseBlocks", () => {
     expect(p).toEqual({ kind: "text", segs: [{ text: "it's 'fine' ' <b>" }] });
   });
 
+  it("leaves no markup behind in link text, even when tags are nested to dodge one pass", () => {
+    const [p] = parseBlocks(`<p><a href="${ISSUE}"><scr<b>ipt>alert(1)<b>y</b></a></p>`);
+    if (p.kind !== "text") throw new Error("expected text");
+    expect(p.segs).toHaveLength(1);
+    expect(p.segs[0].text).not.toMatch(/[<>]/);
+    expect(p.segs[0].text).toContain("alert(1)y");
+  });
+
   it("survives references that name no real character", () => {
     const [p] = parseBlocks("<p>a&#x110000;b&#xD800;c&#0;d&bogus;e</p>");
     expect(p).toEqual({ kind: "text", segs: [{ text: "a\ufffdb\ufffdc\ufffdd&bogus;e" }] });
diff --git a/src/lib/readme.ts b/src/lib/readme.ts
index bade5eb..e2dc86a 100644
--- a/src/lib/readme.ts
+++ b/src/lib/readme.ts
@@ -54,12 +54,24 @@ function decode(s: string): string {
   });
 }
 
+// Removes markup until none is left: one pass over "<scr<b>ipt>" would leave "<script>".
+// The result is only ever rendered as text. Entities are decoded afterwards on purpose, so a
+// README that writes "&lt;b&gt;" still shows the literal text "<b>".
+function stripTags(html: string): string {
+  let out = html;
+  for (let prev = ""; prev !== out; ) {
+    prev = out;
+    out = out.replace(/<[^>]*>/g, "");
+  }
+  return out.replace(/[<>]/g, "");
+}
+
 function segments(html: string): Seg[] {
   const segs: Seg[] = [];
   const re = /<a\s+href="([^"]+)"[^>]*>([\s\S]*?)<\/a>|<[^>]+>|([^<]+)/g;
   for (const m of html.matchAll(re)) {
     if (m[1] !== undefined) {
-      const text = decode(m[2].replace(/<[^>]+>/g, "")).trim();
+      const text = decode(stripTags(m[2])).trim();
       const href = safeHref(m[1]);
       if (text) segs.push(href ? { text, href } : { text });
     } else if (m[3] !== undefined) {