diff --git a/sources/Engine.ts b/sources/Engine.ts
index e08bb1ee1..9525552da 100644
--- a/sources/Engine.ts
+++ b/sources/Engine.ts
@@ -127,7 +127,7 @@ export class Engine {
       throw new UsageError(`This package manager (${descriptor.name}) isn't supported by this corepack build`);
 
     let finalDescriptor = descriptor;
-    if (descriptor.range.match(/^[a-z-]+$/)) {
+    if (/^[a-z-]+$/.test(descriptor.range)) {
       if (!allowTags)
         throw new UsageError(`Packages managers can't be referended via tags in this context`);
 
@@ -151,6 +151,11 @@ export class Engine {
     if (cachedVersion !== null && useCache)
       return {name: finalDescriptor.name, reference: cachedVersion};
 
+    // If the user asked for a specific version, no need to request the list of
+    // available versions from the registry.
+    if (semver.valid(finalDescriptor.range))
+      return {name: finalDescriptor.name, reference: finalDescriptor.range};
+
     const candidateRangeDefinitions = Object.keys(definition.ranges).filter(range => {
       return semverUtils.satisfiesWithPrereleases(finalDescriptor.range, range);
     });
diff --git a/sources/corepackUtils.ts b/sources/corepackUtils.ts
index 94d90d615..93cc79018 100644
--- a/sources/corepackUtils.ts
+++ b/sources/corepackUtils.ts
@@ -1,3 +1,4 @@
+import {createHash}                                            from 'crypto';
 import {once}                                                  from 'events';
 import fs                                                      from 'fs';
 import type {Dir}                                              from 'fs';
@@ -81,21 +82,22 @@ export async function findInstalledVersion(installTarget: string, descriptor: De
 
 export async function installVersion(installTarget: string, locator: Locator, {spec}: {spec: PackageManagerSpec}) {
   const {default: tar} = await import(/* webpackMode: 'eager' */ `tar`);
+  const {version, build} = semver.parse(locator.reference)!;
 
-  const installFolder = path.join(installTarget, locator.name, locator.reference);
+  const installFolder = path.join(installTarget, locator.name, version);
   if (fs.existsSync(installFolder)) {
     debugUtils.log(`Reusing ${locator.name}@${locator.reference}`);
     return installFolder;
   }
 
-  const url = spec.url.replace(`{}`, locator.reference);
+  const url = spec.url.replace(`{}`, version);
 
   // Creating a temporary folder inside the install folder means that we
   // are sure it'll be in the same drive as the destination, so we can
   // just move it there atomically once we are done
 
   const tmpFolder = folderUtils.getTemporaryFolder(installTarget);
-  debugUtils.log(`Installing ${locator.name}@${locator.reference} from ${url} to ${tmpFolder}`);
+  debugUtils.log(`Installing ${locator.name}@${version} from ${url} to ${tmpFolder}`);
   const stream = await httpUtils.fetchUrlStream(url);
 
   const parsedUrl = new URL(url);
@@ -113,8 +115,16 @@ export async function installVersion(installTarget: string, locator: Locator, {s
 
   stream.pipe(sendTo);
 
+  const hash = build[0]
+    ? stream.pipe(createHash(build[0]))
+    : null;
+
   await once(sendTo, `finish`);
 
+  const actualHash = hash?.digest(`hex`);
+  if (actualHash !== build[1])
+    throw new Error(`Mismatch hashes. Expected ${build[1]}, got ${actualHash}`);
+
   await fs.promises.mkdir(path.dirname(installFolder), {recursive: true});
   try {
     await fs.promises.rename(tmpFolder, installFolder);
diff --git a/tests/main.test.ts b/tests/main.test.ts
index 24e9be813..a8010cf83 100644
--- a/tests/main.test.ts
+++ b/tests/main.test.ts
@@ -8,13 +8,38 @@ beforeEach(async () => {
   process.env.COREPACK_HOME = npath.fromPortablePath(await xfs.mktempPromise());
 });
 
+it(`should refuse to download a package manager if the hash doesn't match`, async () => {
+  await xfs.mktempPromise(async cwd => {
+    await xfs.writeJsonPromise(ppath.join(cwd, `package.json` as Filename), {
+      packageManager: `yarn@1.22.4+sha1.deadbeef`,
+    });
+
+    await expect(runCli(cwd, [`yarn`, `--version`])).resolves.toMatchObject({
+      exitCode: 1,
+      stdout: /Mismatch hashes/,
+    });
+  });
+});
+
 const testedPackageManagers: Array<[string, string]> = [
   [`yarn`, `1.22.4`],
+  [`yarn`, `1.22.4+sha1.01c1197ca5b27f21edc8bc472cd4c8ce0e5a470e`],
+  [`yarn`, `1.22.4+sha224.0d6eecaf4d82ec12566fdd97143794d0f0c317e0d652bd4d1b305430`],
   [`yarn`, `2.0.0-rc.30`],
+  [`yarn`, `2.0.0-rc.30+sha1.4f0423b01bcb57f8e390b4e0f1990831f92dd1da`],
+  [`yarn`, `2.0.0-rc.30+sha224.0e7a64468c358596db21c401ffeb11b6534fce7367afd3ae640eadf1`],
   [`yarn`, `3.0.0-rc.2`],
+  [`yarn`, `3.0.0-rc.2+sha1.694bdad81703169e203febd57f9dc97d3be867bd`],
+  [`yarn`, `3.0.0-rc.2+sha224.f83f6d1cbfac10ba6b516a62ccd2a72ccd857aa6c514d1cd7185ec60`],
   [`pnpm`, `4.11.6`],
+  [`pnpm`, `4.11.6+sha1.7cffc04295f4db4740225c6c37cc345eb923c06a`],
+  [`pnpm`, `4.11.6+sha224.7783c4b01916b7a69e6ff05d328df6f83cb7f127e9c96be88739386d`],
   [`pnpm`, `6.6.2`],
+  [`pnpm`, `6.6.2+sha1.7b4d6b176c1b93b5670ed94c24babb7d80c13854`],
+  [`pnpm`, `6.6.2+sha224.eb5c0acad3b0f40ecdaa2db9aa5a73134ad256e17e22d1419a2ab073`],
   [`npm`, `6.14.2`],
+  [`npm`, `6.14.2+sha1.f057d35cd4792c4c511bb1fa332edb43143d07b0`],
+  [`npm`, `6.14.2+sha224.50512c1eb404900ee78586faa6d756b8d867ff46a328e6fb4cdf3a87`],
 ];
 
 for (const [name, version] of testedPackageManagers) {
@@ -26,7 +51,7 @@ for (const [name, version] of testedPackageManagers) {
 
       await expect(runCli(cwd, [name, `--version`])).resolves.toMatchObject({
         exitCode: 0,
-        stdout: `${version}\n`,
+        stdout: `${version.split(`+`, 1)[0]}\n`,
       });
     });
   });
@@ -136,17 +161,17 @@ it(`should use the pinned version when local projects don't list any spec`, asyn
     });
 
     await expect(runCli(cwd, [`yarn`, `--version`])).resolves.toMatchObject({
-      stdout: `${config.definitions.yarn.default}\n`,
+      stdout: `${config.definitions.yarn.default.split(`+`, 1)[0]}\n`,
       exitCode: 0,
     });
 
     await expect(runCli(cwd, [`pnpm`, `--version`])).resolves.toMatchObject({
-      stdout: `${config.definitions.pnpm.default}\n`,
+      stdout: `${config.definitions.pnpm.default.split(`+`, 1)[0]}\n`,
       exitCode: 0,
     });
 
     await expect(runCli(cwd, [`npm`, `--version`])).resolves.toMatchObject({
-      stdout: `${config.definitions.npm.default}\n`,
+      stdout: `${config.definitions.npm.default.split(`+`, 1)[0]}\n`,
       exitCode: 0,
     });
   });