diff --git a/packages/compiler/src/diagnostics/diagnostic.ts b/packages/compiler/src/diagnostics/diagnostic.ts
index 039d94977fd..4994f763b0d 100644
--- a/packages/compiler/src/diagnostics/diagnostic.ts
+++ b/packages/compiler/src/diagnostics/diagnostic.ts
@@ -2206,11 +2206,16 @@ export function unsupportedNativeApiDiag(
   };
 }
 
-export function unsupportedPackageImportDiag(pkg: string, loc: SrcLoc): ScrDiagnostic {
+export function unsupportedPackageImportDiag(
+  pkg: string,
+  loc: SrcLoc,
+  hint?: string,
+): ScrDiagnostic {
   return npmStaticRefusalDiag(
     pkg,
     "its implementation is not part of the compiled module graph",
     loc,
+    hint,
   );
 }
 
@@ -2222,6 +2227,16 @@ export function unsupportedPackageValueDiag(pkg: string, loc: SrcLoc): ScrDiagno
   );
 }
 
+/** The package a declaration-only `@types/<name>` package types: resolution
+ * can answer the types package for a program that imports `<name>`, and the
+ * diagnostic must name what the program imports (`@types/scope__name` types
+ * `@scope/name`). Any other name is returned as is. */
+export function runtimePackageName(pkg: string): string {
+  if (!pkg.startsWith("@types/")) return pkg;
+  const bare = pkg.slice("@types/".length);
+  return bare.includes("__") ? `@${bare.replace("__", "/")}` : bare;
+}
+
 export function npmStaticRefusalDiag(
   pkg: string,
   detail: string,
@@ -2230,7 +2245,7 @@ export function npmStaticRefusalDiag(
 ): ScrDiagnostic {
   return {
     code: "SC2013",
-    message: `cannot compile npm package '${pkg}' statically: ${detail}`,
+    message: `cannot compile npm package '${runtimePackageName(pkg)}' statically: ${detail}`,
     loc,
     milestone: "later",
     hint:
diff --git a/packages/compiler/src/frontend/lowering/lower-stdlib.ts b/packages/compiler/src/frontend/lowering/lower-stdlib.ts
index 4bcbea62c57..1cffce99296 100644
--- a/packages/compiler/src/frontend/lowering/lower-stdlib.ts
+++ b/packages/compiler/src/frontend/lowering/lower-stdlib.ts
@@ -45,6 +45,7 @@ import {
 import {
   type ScrDiagnostic,
   unsupportedNativeApiDiag,
+  runtimePackageName,
   unsupportedPackageImportDiag,
   unsupportedPackageValueDiag,
 } from "../../diagnostics/diagnostic.js";
@@ -2356,7 +2357,8 @@ function uncompiledImportPackage(lowerer: Lowerer, call: ts.CallExpression): str
   if (specifier === null) return null;
   const file = ts.getSourceFileOfNode(call).fileName;
   if (lowerer.dynImports.get(dynImportKey(file, specifier, !literal)) !== undefined) return null;
-  return resolveNpmImport(file, specifier)?.packageName ?? null;
+  const npm = resolveNpmImport(file, specifier);
+  return npm === null ? null : runtimePackageName(npm.packageName);
 }
 
 /** The package a refusal names as outside the compiled module graph
@@ -2425,7 +2427,14 @@ function lowerResolvedImport(
     // call (lower-node-island.ts, lowerIslandLoadCall).
     const npm = resolveNpmImport(ts.getSourceFileOfNode(call).fileName, specifier);
     if (npm !== null) {
-      lowerer.pushDiag(unsupportedPackageImportDiag(npm.packageName, locOf(call)));
+      lowerer.pushDiag(
+        unsupportedPackageImportDiag(
+          runtimePackageName(npm.packageName),
+          locOf(call),
+          "no static import names this package, so it is not compiled: add a static import of it " +
+            "(`import x from 'pkg'`) so it joins the module graph, or allow a Node island for it",
+        ),
+      );
       throw new PoisonError();
     }
     lowerer.refuseUnsupportedApi("'import()'", call);
diff --git a/tests/harness/lazy-package-import.test.ts b/tests/harness/lazy-package-import.test.ts
index 4ec2a243f8d..275c3a4c7d6 100644
--- a/tests/harness/lazy-package-import.test.ts
+++ b/tests/harness/lazy-package-import.test.ts
@@ -4,7 +4,7 @@
  * uncompiled package reports, and that refusal names the package. Under the
  * automatic policy the package then runs in a Node island (corpus 9537 runs
  * that against Node); with islands off the refusal is the build's error. */
-import { cpSync, mkdtempSync, rmSync } from "node:fs";
+import { cpSync, mkdirSync, mkdtempSync, rmSync, writeFileSync } from "node:fs";
 import { tmpdir } from "node:os";
 import { join } from "node:path";
 import { afterAll, expect, test } from "vitest";
@@ -33,3 +33,45 @@ test("with islands off, the build error names the lazily imported package", asyn
   );
   expect(result.diagnostics.map((d) => d.code)).not.toContain("SC2012");
 }, 120_000);
+
+test("the refusal names the imported package, not its @types package, and hints at a static import", async () => {
+  const copy = mkdtempSync(join(tmpdir(), "scriptc-lazy-types-"));
+  copies.push(copy);
+  const write = (file: string, text: string): void => {
+    mkdirSync(join(copy, file, ".."), { recursive: true });
+    writeFileSync(join(copy, file), text);
+  };
+  write("package.json", '{"name":"app","private":true,"type":"module"}\n');
+  write(
+    "node_modules/tiny-ms/package.json",
+    '{"name":"tiny-ms","version":"1.0.0","main":"index.js"}\n',
+  );
+  write("node_modules/tiny-ms/index.js", "module.exports = (s) => s.length;\n");
+  write(
+    "node_modules/@types/tiny-ms/package.json",
+    '{"name":"@types/tiny-ms","version":"1.0.0","types":"index.d.ts"}\n',
+  );
+  write(
+    "node_modules/@types/tiny-ms/index.d.ts",
+    "declare function ms(s: string): number;\nexport = ms;\n",
+  );
+  write(
+    "main.ts",
+    'async function main() {\n  const m = await import("tiny-ms");\n  console.log(m.default("abc"));\n}\nmain();\n',
+  );
+  const result = await compile(join(copy, "main.ts"), {
+    outPath: join(copy, "main"),
+    outDir: copy,
+    nodeIslands: { mode: "off" },
+  });
+  expect(result.ok).toBe(false);
+  if (result.ok) return;
+  const refusals = result.diagnostics.filter((d) => d.code === "SC2013");
+  expect(refusals.length).toBeGreaterThan(0);
+  for (const refusal of refusals) {
+    expect(refusal.message).toBe(
+      "cannot compile npm package 'tiny-ms' statically: its implementation is not part of the compiled module graph",
+    );
+  }
+  expect(refusals[0]?.hint).toContain("add a static import");
+}, 120_000);