diff --git a/lib/helpers/versions.js b/lib/helpers/versions.js
index 55de05b094f71e431600360710693320a1b8dc25..1b38e22891fd361f3faa287c6fcc97211457f737 100644
--- a/lib/helpers/versions.js
+++ b/lib/helpers/versions.js
@@ -124,6 +124,12 @@ function determineUpgrades(dep, currentVersion, config) {
         // Add a tilde before that version number
         return Object.assign(upgrade, { newVersion: `~${minSatisfying}` });
       } else if (currentSemver.operator === '^') {
+        // Special case where major and minor are 0
+        if (major === '0' && minor === '0') {
+          return Object.assign(upgrade, {
+            newVersion: `^${upgrade.newVersion}`,
+          });
+        }
         // If version is < 1, then semver treats ^ same as ~
         const newRange = major === '0' ? `${major}.${minor}` : `${major}`;
         const minSatisfying = semver.minSatisfying(versionList, newRange);
diff --git a/test/_fixtures/npm/02.json b/test/_fixtures/npm/02.json
new file mode 100644
index 0000000000000000000000000000000000000000..89d9e47c67432cd96b2cc09af56600bc92e09d7a
--- /dev/null
+++ b/test/_fixtures/npm/02.json
@@ -0,0 +1 @@
+{"_id":"@types/helmet","_rev":"30-e35b3124b21d9e35d55d998fc9e9cb1c","name":"@types/helmet","description":"TypeScript definitions for helmet","dist-tags":{"latest":"0.0.35","ts2.0":"0.0.35","ts2.1":"0.0.35","ts2.2":"0.0.35","ts2.3":"0.0.35"},"versions":{"0.0.15-alpha":{"name":"@types/helmet","version":"0.0.15-alpha","description":"Type definitions for helmet from https://www.github.com/DefinitelyTyped/DefinitelyTyped","main":"","scripts":{},"author":{"name":"Cyril Schumacher","email":"https://github.com/cyrilschumacher"},"license":"MIT","typings":"index.d.ts","dependencies":{},"_id":"@types/helmet@0.0.15-alpha","_shasum":"246f328b3a76c8e6f1f400beaf52aa4e75f94399","_from":"output\\helmet","_resolved":"file:output\\helmet","_npmVersion":"3.8.2","_nodeVersion":"5.5.0","_npmUser":{"name":"types","email":"ryan.cavanaugh@microsoft.com"},"dist":{"shasum":"246f328b3a76c8e6f1f400beaf52aa4e75f94399","tarball":"https://registry.npmjs.org/@types/helmet/-/helmet-0.0.15-alpha.tgz"},"maintainers":[{"name":"types","email":"ryan.cavanaugh@microsoft.com"}],"_npmOperationalInternal":{"host":"packages-16-east.internal.npmjs.com","tmp":"tmp/helmet-0.0.15-alpha.tgz_1463461756136_0.20830343128181994"},"directories":{}},"0.0.16-alpha":{"name":"@types/helmet","version":"0.0.16-alpha","description":"Type definitions for helmet from https://www.github.com/DefinitelyTyped/DefinitelyTyped","main":"","scripts":{},"author":{"name":"Cyril 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helmet","main":"","scripts":{},"author":{"name":"Cyril Schumacher","email":"https://github.com/cyrilschumacher"},"repository":{"type":"git","url":"https://www.github.com/DefinitelyTyped/DefinitelyTyped.git"},"license":"MIT","typings":"index.d.ts","dependencies":{"@types/express":"4.0.*"},"_id":"@types/helmet@0.0.28","_shasum":"4dc56f58c51dea0568d634773b1ecb8d39e87111","_from":"output\\helmet","_resolved":"file:output\\helmet","_npmVersion":"3.10.3","_nodeVersion":"6.3.0","_npmUser":{"name":"types","email":"ts-npm-types@microsoft.com"},"dist":{"shasum":"4dc56f58c51dea0568d634773b1ecb8d39e87111","tarball":"https://registry.npmjs.org/@types/helmet/-/helmet-0.0.28.tgz"},"maintainers":[{"name":"types","email":"ryan.cavanaugh@microsoft.com"}],"_npmOperationalInternal":{"host":"packages-12-west.internal.npmjs.com","tmp":"tmp/helmet-0.0.28.tgz_1468507867621_0.08634940208867192"},"directories":{}},"0.0.29":{"name":"@types/helmet","version":"0.0.29","description":"TypeScript definitions for 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<https://github.com/EvanHahn>","main":"","repository":{"type":"git","url":"https://www.github.com/DefinitelyTyped/DefinitelyTyped.git"},"scripts":{},"dependencies":{"@types/express":"4.0.*"},"typings":"index.d.ts","_id":"@types/helmet@0.0.30","dist":{"shasum":"9cfabb7f4f62de675f38e61600d6059dec0abf0a","tarball":"https://registry.npmjs.org/@types/helmet/-/helmet-0.0.30.tgz"},"maintainers":[{"name":"types","email":"ryan.cavanaugh@microsoft.com"}],"_npmUser":{"name":"types","email":"ts-npm-types@microsoft.com"},"_npmOperationalInternal":{"host":"packages-12-west.internal.npmjs.com","tmp":"tmp/helmet-0.0.30.tgz_1471620439944_0.8102214504033327"},"directories":{}},"0.0.31":{"name":"@types/helmet","version":"0.0.31","description":"TypeScript definitions for helmet","license":"MIT","author":"Cyril Schumacher <https://github.com/cyrilschumacher>, Evan Hahn 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Schumacher","url":"https://github.com/cyrilschumacher"},{"name":"Evan Hahn","url":"https://github.com/EvanHahn"}],"main":"","repository":{"type":"git","url":"https://www.github.com/DefinitelyTyped/DefinitelyTyped.git"},"scripts":{},"dependencies":{"@types/express":"*"},"peerDependencies":{},"typesPublisherContentHash":"6c266e012437a4fe288dd08fbbc0d1f25a7b66848512268f7c149f08398e10b0","typeScriptVersion":"2.0","_id":"@types/helmet@0.0.35","dist":{"shasum":"b5f035063180c2c1f43122aba2612c9ed9466dc0","tarball":"https://registry.npmjs.org/@types/helmet/-/helmet-0.0.35.tgz"},"maintainers":[{"name":"types","email":"ryan.cavanaugh@microsoft.com"}],"_npmUser":{"name":"types","email":"ts-npm-types@microsoft.com"},"_npmOperationalInternal":{"host":"packages-12-west.internal.npmjs.com","tmp":"tmp/helmet-0.0.35.tgz_1493312346222_0.434226565528661"},"directories":{}}},"readme":"# Installation\r\n> `npm install --save @types/helmet`\r\n\r\n# Summary\r\nThis package contains type definitions for helmet (https://github.com/helmetjs/helmet).\r\n\r\n# Details\r\nFiles were exported from https://www.github.com/DefinitelyTyped/DefinitelyTyped/tree/master/types/helmet\r\n\r\nAdditional Details\r\n * Last updated: Thu, 27 Apr 2017 16:58:33 GMT\r\n * Dependencies: express\r\n * Global values: none\r\n\r\n# Credits\r\nThese definitions were written by Cyril Schumacher <https://github.com/cyrilschumacher>, Evan Hahn <https://github.com/EvanHahn>.\r\n","maintainers":[{"name":"types","email":"ryan.cavanaugh@microsoft.com"}],"time":{"modified":"2017-04-27T16:59:07.470Z","created":"2016-05-17T05:09:19.506Z","0.0.15-alpha":"2016-05-17T05:09:19.506Z","0.0.16-alpha":"2016-05-19T21:08:52.726Z","0.0.21-alpha":"2016-05-20T19:46:26.550Z","0.0.22-alpha":"2016-05-25T05:04:43.020Z","0.0.23-alpha":"2016-07-01T19:32:10.873Z","0.0.24-alpha":"2016-07-01T23:00:52.202Z","0.0.25-alpha":"2016-07-02T02:33:35.727Z","0.0.26-alpha":"2016-07-04T00:22:49.651Z","0.0.27-alpha":"2016-07-08T20:21:24.763Z","0.0.28":"2016-07-14T14:51:09.691Z","0.0.29":"2016-08-02T15:54:33.151Z","0.0.30":"2016-08-19T15:27:21.483Z","0.0.31":"2016-08-25T18:44:32.543Z","0.0.32":"2016-09-19T17:41:40.645Z","0.0.33":"2016-10-05T20:57:33.393Z","0.0.34":"2017-03-10T06:08:16.223Z","0.0.35":"2017-04-27T16:59:06.479Z"},"license":"MIT","readmeFilename":"","repository":{"type":"git","url":"https://www.github.com/DefinitelyTyped/DefinitelyTyped.git"},"users":{"hongbo-miao":true},"contributors":[{"name":"Cyril 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\ No newline at end of file
diff --git a/test/helpers/versions.spec.js b/test/helpers/versions.spec.js
index 046096233c5ae07484fec43c101c01003a27619b..f6efd2704c1f74d605879a7eef46dbe11124fc31 100644
--- a/test/helpers/versions.spec.js
+++ b/test/helpers/versions.spec.js
@@ -1,5 +1,6 @@
 const versionsHelper = require('../../lib/helpers/versions');
 const qJson = require('../_fixtures/npm/01.json');
+const helmetJson = require('../_fixtures/npm/02.json');
 
 let defaultConfig;
 
@@ -453,6 +454,28 @@ describe('helpers/versions', () => {
         )
         .should.eql(upgradeVersions);
     });
+    it('should treat zero zero tilde ranges as 0.0.x', () => {
+      const config = Object.assign({}, defaultConfig, { pinVersions: false });
+      expect(
+        versionsHelper.determineUpgrades(helmetJson, '~0.0.34', config)
+      ).toEqual([]);
+    });
+    it('should treat zero zero caret ranges as pinned', () => {
+      const config = Object.assign({}, defaultConfig, { pinVersions: false });
+      const upgradeVersions = [
+        {
+          newVersion: '^0.0.35',
+          newVersionMajor: 0,
+          upgradeType: 'minor',
+          changeLogFromVersion: '0.0.34',
+          changeLogToVersion: '0.0.35',
+          isRange: true,
+        },
+      ];
+      expect(
+        versionsHelper.determineUpgrades(helmetJson, '^0.0.34', config)
+      ).toEqual(upgradeVersions);
+    });
   });
   describe('.isRange(input)', () => {
     it('rejects simple semver', () => {