diff --git a/packages/header-parser/src/index.ts b/packages/header-parser/src/index.ts
index 4129694084..8c48036986 100644
--- a/packages/header-parser/src/index.ts
+++ b/packages/header-parser/src/index.ts
@@ -1,6 +1,5 @@
 import pm = require("parsimmon");
 import { AllTypeScriptVersion, TypeScriptVersion } from "@definitelytyped/typescript-versions";
-import assert = require("assert");
 
 /*
 
@@ -46,9 +45,7 @@ export function makeTypesVersionsForPackageJson(typesVersions: readonly TypeScri
   oldestFirst.sort((v1, v2) => (v1 > v2 ? 1 : v1 < v2 ? -1 : 0));
   const out: { [key: string]: { readonly "*": readonly string[] } } = {};
   for (const version of oldestFirst) {
-    const next = TypeScriptVersion.next(version);
-    assert(!!next, `ts${version} is too new: it covers all versions of typescript`);
-    out[`<${next}.0-0`] = { "*": [`ts${version}/*`] };
+    out[`<=${version}`] = { "*": [`ts${version}/*`] };
   }
   return out;
 }
diff --git a/packages/header-parser/test/index.test.ts b/packages/header-parser/test/index.test.ts
index 5e863958d1..046b0a3da9 100644
--- a/packages/header-parser/test/index.test.ts
+++ b/packages/header-parser/test/index.test.ts
@@ -204,24 +204,24 @@ describe("makeTypesVersionsForPackageJson", () => {
   });
   it("works for one version", () => {
     expect(makeTypesVersionsForPackageJson(["4.3"])).toEqual({
-      "<4.4.0-0": {
+      "<=4.3": {
         "*": ["ts4.3/*"],
       },
     });
   });
   it("orders versions old to new  with old-to-new input", () => {
     expect(JSON.stringify(makeTypesVersionsForPackageJson(["4.2", "4.3", "4.6"]), undefined, 4)).toEqual(`{
-    "<4.3.0-0": {
+    "<=4.2": {
         "*": [
             "ts4.2/*"
         ]
     },
-    "<4.4.0-0": {
+    "<=4.3": {
         "*": [
             "ts4.3/*"
         ]
     },
-    "<4.7.0-0": {
+    "<=4.6": {
         "*": [
             "ts4.6/*"
         ]
@@ -230,28 +230,23 @@ describe("makeTypesVersionsForPackageJson", () => {
   });
   it("orders versions old to new  with new-to-old input", () => {
     expect(JSON.stringify(makeTypesVersionsForPackageJson(["4.6", "4.3", "4.2"]), undefined, 4)).toEqual(`{
-    "<4.3.0-0": {
+    "<=4.2": {
         "*": [
             "ts4.2/*"
         ]
     },
-    "<4.4.0-0": {
+    "<=4.3": {
         "*": [
             "ts4.3/*"
         ]
     },
-    "<4.7.0-0": {
+    "<=4.6": {
         "*": [
             "ts4.6/*"
         ]
     }
 }`);
   });
-  it("asserts when trying to redirect from newest version and below", () => {
-    expect(() => makeTypesVersionsForPackageJson(["5.0"])).toThrow(
-      /ts5.0 is too new: it covers all versions of typescript/
-    );
-  });
 });
 
 function dedent(strings: TemplateStringsArray): string {