diff --git a/lsp/src/typescript-blocks.test.ts b/lsp/src/typescript-blocks.test.ts
index 63698670..29901206 100644
--- a/lsp/src/typescript-blocks.test.ts
+++ b/lsp/src/typescript-blocks.test.ts
@@ -169,6 +169,29 @@ describe("extractTypeScriptBlocks", () => {
     ).toEqual([]);
   });
 
+  it("matches tag names in any ASCII case, as an HTML parser does", () => {
+    const html =
+      '<SCRIPT type="text/typescript">let a = 1;</Script ><TEXTAREA><script type="text/typescript">let b;</script></TextArea><sCrIpT type="text/typescript">let c = 1;</SCRIPT>';
+    expect(extractTypeScriptBlocks(html).map((block) => block.content)).toEqual(
+      ["let a = 1;", "let c = 1;"],
+    );
+  });
+
+  it("places a block after text whose lowercase is longer, such as a dotted capital I", () => {
+    // "İ".toLowerCase() is two characters: offsets taken from a lowercased copy of the page land past the block.
+    const before = "<p>İstanbul İzmir</p>\n";
+    const html = `${before}<script type="text/typescript">const city: string = "x";</script>`;
+    const [block] = extractTypeScriptBlocks(html);
+    expect(block.content).toBe('const city: string = "x";');
+    expect(
+      html.slice(block.contentStart, block.contentStart + block.content.length),
+    ).toBe(block.content);
+    const [script] = extractPageScopeScripts(
+      html.replace("text/typescript", "text/javascript"),
+    );
+    expect(script.content).toBe('const city: string = "x";');
+  });
+
   it("skips the scan when the file never mentions text/typescript", () => {
     expect(mayHaveTypeScriptBlocks("<script>let a;</script>")).toBe(false);
     expect(mayHaveTypeScriptBlocks('<script type="Text/TypeScript">')).toBe(
diff --git a/lsp/src/typescript-blocks.ts b/lsp/src/typescript-blocks.ts
index b656d839..b236f3cc 100644
--- a/lsp/src/typescript-blocks.ts
+++ b/lsp/src/typescript-blocks.ts
@@ -78,13 +78,29 @@ function findOpenTagEnd(html: string, from: number): number {
   return -1;
 }
 
-/** The index of `</name` (followed by a tag-name end) at or after `from`, or -1. */
-function findCloseTag(lower: string, from: number, name: string): number {
-  const needle = `</${name}`;
-  for (let at = lower.indexOf(needle, from); at >= 0;) {
-    if (isTagNameEnd(lower[at + needle.length])) return at;
-    at = lower.indexOf(needle, at + 1);
-  }
+/**
+ * Whether `html` holds `name` (lowercase ASCII letters) at `at`, in any ASCII case, as an HTML parser compares tag
+ * names. Setting bit 0x20 lowercases an ASCII letter and leaves every other code unequal to a lowercase letter.
+ */
+function hasTagNameAt(html: string, at: number, name: string): boolean {
+  if (at + name.length > html.length) return false;
+  for (let k = 0; k < name.length; k++)
+    if ((html.charCodeAt(at + k) | 0x20) !== name.charCodeAt(k)) return false;
+  return true;
+}
+
+/** The index of `</name` (any ASCII case, followed by a tag-name end) at or after `from`, or -1. */
+function findCloseTag(html: string, from: number, name: string): number {
+  for (
+    let at = html.indexOf("</", from);
+    at >= 0;
+    at = html.indexOf("</", at + 2)
+  )
+    if (
+      hasTagNameAt(html, at + 2, name) &&
+      isTagNameEnd(html[at + 2 + name.length])
+    )
+      return at;
   return -1;
 }
 
@@ -105,16 +121,19 @@ interface ScriptElement {
 /**
  * Every `<script>` element of an HTML file, in source order. A script inside an HTML comment or another raw-text
  * element, and one whose tag or element never closes, is not one.
+ *
+ * Tag names are compared in place, in ASCII case only. Lowercasing the page instead copied all of it on every scan
+ * (the language server scans on each keystroke), and Unicode lowercasing can change a string's length ("İ" becomes
+ * two characters), which moved every offset after it.
  */
 function scanScripts(html: string): ScriptElement[] {
   const scripts: ScriptElement[] = [];
-  const lower = html.toLowerCase();
   let i = 0;
   while (i < html.length) {
-    const lt = lower.indexOf("<", i);
+    const lt = html.indexOf("<", i);
     if (lt < 0) break;
-    if (lower.startsWith("<!--", lt)) {
-      const end = lower.indexOf("-->", lt + 4);
+    if (html.startsWith("<!--", lt)) {
+      const end = html.indexOf("-->", lt + 4);
       // An unclosed comment runs to the end of the file, as in a browser.
       if (end < 0) break;
       i = end + 3;
@@ -122,8 +141,8 @@ function scanScripts(html: string): ScriptElement[] {
     }
     const name = RAW_TEXT_ELEMENTS.find(
       (candidate) =>
-        lower.startsWith(candidate, lt + 1) &&
-        isTagNameEnd(lower[lt + 1 + candidate.length]),
+        hasTagNameAt(html, lt + 1, candidate) &&
+        isTagNameEnd(html[lt + 1 + candidate.length]),
     );
     if (!name) {
       i = lt + 1;
@@ -132,7 +151,7 @@ function scanScripts(html: string): ScriptElement[] {
     const tagEnd = findOpenTagEnd(html, lt + 1 + name.length);
     if (tagEnd < 0) break;
     const contentStart = tagEnd + 1;
-    const close = findCloseTag(lower, contentStart, name);
+    const close = findCloseTag(html, contentStart, name);
     // An element that never closes swallows the rest of the file; nothing after it is a tag.
     if (close < 0) break;
     if (name === "script") {
diff --git a/lsp/src/typescript-service.linear-time.test.ts b/lsp/src/typescript-service.linear-time.test.ts
index 2ede2541..16a01c94 100644
--- a/lsp/src/typescript-service.linear-time.test.ts
+++ b/lsp/src/typescript-service.linear-time.test.ts
@@ -22,14 +22,26 @@ afterAll(() => fixture.remove());
 // cross it for some fixtures: 8,000/32,000 unclosed-comment units are 56 KB/224 KB.
 const SMALL_SCAN_CHARACTERS = 256_000;
 // A fixture that is one long run of text is scanned by a native search at memory speed, so its cost per character
-// is the cost of a cache miss. At 256 KB against 1 MB the small input fits a CI runner's per-core cache and the
-// large one does not, and linear work measured a growth of 12.6 there. At 4 MB against 16 MB both are past it.
+// is the CPU's cost of reading memory, which changes where an input stops fitting a cache. Where that is depends on
+// the runner: the same linear search read 3.0 at 256 KB against 1 MB, 5.2 to 5.6 at 1 MB against 4 MB and 4.4 at 4 MB
+// against 16 MB on one CI runner, and checks of it at 4 MB against 16 MB read 12.2 to 16.6 on others. So such a
+// check is measured against a native search over the same two texts (`MEMORY_BOUND_REFERENCE`), which pays the same
+// cost of reading them: a linear scan grows about as much as it does (1), and work that rescans the text for each
+// character about four times as much. Both texts stay past the large-object boundary, and large enough that each run
+// is a few milliseconds of reading.
 const MEMORY_BOUND_SCAN_CHARACTERS = 4_000_000;
+/** One native pass over all of `text`: U+0001 never occurs in the fixtures. */
+const MEMORY_BOUND_REFERENCE = (text: string) => text.indexOf("\u0001");
+/** How much more a memory-bound scan grows than reading its texts does. Linear reads about 1, quadratic about 4. */
+const MAX_GROWTH_OVER_READING = 2;
 const scanGrowth = (
   html: (count: number) => string,
   scan: (text: string) => unknown,
-  smallCharacters = SMALL_SCAN_CHARACTERS,
+  memoryBound = false,
 ): number => {
+  const smallCharacters = memoryBound
+    ? MEMORY_BOUND_SCAN_CHARACTERS
+    : SMALL_SCAN_CHARACTERS;
   const prefixLength = html(0).length;
   const unitLength = html(1).length - prefixLength;
   expect(unitLength).toBeGreaterThan(0);
@@ -38,12 +50,25 @@ const scanGrowth = (
   const large = html(4 * smallCount);
   expect(small.length).toBeGreaterThanOrEqual(smallCharacters);
   expect(large.length - prefixLength).toBe(4 * (small.length - prefixLength));
-  return growthOf(
+  if (memoryBound) expect(large.includes("\u0001")).toBe(false);
+  const growth = growthOf(
     () => scan(small),
     () => scan(large),
   );
+  if (!memoryBound) return growth;
+  return (
+    growth /
+    growthOf(
+      () => MEMORY_BOUND_REFERENCE(small),
+      () => MEMORY_BOUND_REFERENCE(large),
+    )
+  );
 };
 
+/** The bar a scan's growth must stay under: over reading its texts for a memory-bound one, 8 otherwise. */
+const maxScanGrowth = (memoryBound = false) =>
+  memoryBound ? MAX_GROWTH_OVER_READING : 8;
+
 /** A page of `count` client blocks, each with a little typed code. */
 const pageOf = (count: number, edited: string) =>
   Array.from(
@@ -86,7 +111,8 @@ describe("TypeScript block diagnostics: linear time", () => {
     LINEAR_TIME_TIMEOUT_MS,
   );
 
-  const scans: Array<[string, (n: number) => string, number?]> = [
+  // The third entry marks a memory-bound fixture (see MEMORY_BOUND_SCAN_CHARACTERS).
+  const scans: Array<[string, (n: number) => string, boolean?]> = [
     [
       "script tags that never close",
       (n) => `text/typescript ${'<script type="text/typescript">'.repeat(n)}`,
@@ -98,7 +124,7 @@ describe("TypeScript block diagnostics: linear time", () => {
     [
       "a quote that never ends",
       (n) => `text/typescript <script type="${"a".repeat(n)}`,
-      MEMORY_BOUND_SCAN_CHARACTERS,
+      true,
     ],
     [
       "many comments",
@@ -121,24 +147,24 @@ describe("TypeScript block diagnostics: linear time", () => {
 
   it.each(scans)(
     "finds blocks in linear time with %s",
-    (_label, html, smallCharacters) => {
+    (_label, html, memoryBound) => {
       expect(
-        scanGrowth(html, extractTypeScriptBlocks, smallCharacters),
-      ).toBeLessThan(8);
+        scanGrowth(html, extractTypeScriptBlocks, memoryBound),
+      ).toBeLessThan(maxScanGrowth(memoryBound));
     },
     LINEAR_TIME_TIMEOUT_MS,
   );
 
   it.each(scans)(
     "finds the page's classic scripts in linear time with %s",
-    (_label, html, smallCharacters) => {
+    (_label, html, memoryBound) => {
       expect(
         scanGrowth(
           (n) => html(n).replaceAll("text/typescript", "text/javascript"),
           extractPageScopeScripts,
-          smallCharacters,
+          memoryBound,
         ),
-      ).toBeLessThan(8);
+      ).toBeLessThan(maxScanGrowth(memoryBound));
     },
     LINEAR_TIME_TIMEOUT_MS,
   );