diff --git a/buildutils/src/update-dependency.ts b/buildutils/src/update-dependency.ts
index 553b6aa48536..3e0b9236e641 100755
--- a/buildutils/src/update-dependency.ts
+++ b/buildutils/src/update-dependency.ts
@@ -12,32 +12,57 @@ import commander from 'commander';
 import semver from 'semver';
 
 let versionCache = new Map();
-const tags = /^([~^]?)([\w\-.]*)$/;
 
+/**
+ * Matches a simple semver range, where the version number could be an npm tag.
+ */
+const SEMVER_RANGE = /^(~|\^|=|<|>|<=|>=)?([\w\-.]*)$/;
+
+/**
+ * Get the specifier we should use
+ *
+ * @param currentSpecifier - The current package version.
+ * @param suggestedSpecifier - The package version we would like to use.
+ *
+ * #### Notes
+ * If the suggested specifier is not a valid range, we assume it is of the
+ * form ${RANGE}${TAG}, where TAG is an npm tag (such as 'latest') and RANGE
+ * is either a semver range indicator (one of `~, ^, >, <, =, >=, <=`), or is
+ * not given (in which case the current specifier range prefix is used).
+ */
 async function getSpecifier(
   currentSpecifier: string,
   suggestedSpecifier: string
 ) {
-  // we have an special case where `latest` will use the same current specifier
-  // e.g. when using latest:
-  //    ^current should result in ^new
-  //    ~current should result in ~new
+  console.log(`current: ${currentSpecifier}`);
+  console.log(`suggested: ${suggestedSpecifier}`);
+  if (semver.validRange(suggestedSpecifier)) {
+    return suggestedSpecifier;
+  }
 
-  if (semver.validRange(suggestedSpecifier) === null) {
-    // We have a tag, with possibly a range specifier, such as ^latest
-    let specifier = suggestedSpecifier;
-    if (specifier === 'latest') {
-      specifier = currentSpecifier;
-    }
-    let match = specifier.match(tags);
+  // The suggested specifier is not a valid range, so we assume it
+  // references a tag
+  let [, suggestedSigil, suggestedTag] =
+    suggestedSpecifier.match(SEMVER_RANGE) ?? [];
+
+  if (!suggestedTag) {
+    throw Error(`Invalid version specifier: ${suggestedSpecifier}`);
+  }
+
+  // A tag with no sigil adopts the sigil from the current specification
+  if (!suggestedSigil) {
+    let match = currentSpecifier.match(SEMVER_RANGE);
     if (match === null) {
-      throw Error(`Invalid version specifier: ${specifier}`);
+      throw Error(
+        `Current version range is not recognized: ${currentSpecifier}`
+      );
+    }
+    let [, currentSigil] = match;
+    if (currentSigil) {
+      suggestedSigil = currentSigil;
     }
-    specifier = match[1] + suggestedSpecifier;
-    return specifier;
-  } else {
-    return suggestedSpecifier;
   }
+  return `${suggestedSigil}${suggestedTag}`;
 }
 
 async function getVersion(pkg: string, specifier: string) {
@@ -47,7 +72,7 @@ async function getVersion(pkg: string, specifier: string) {
   }
   if (semver.validRange(specifier) === null) {
     // We have a tag, with possibly a range specifier, such as ^latest
-    let match = specifier.match(tags);
+    let match = specifier.match(SEMVER_RANGE);
     if (match === null) {
       throw Error(`Invalid version specifier: ${specifier}`);
     }
@@ -70,10 +95,10 @@ async function getVersion(pkg: string, specifier: string) {
  */
 function subset(range1: string, range2: string): boolean {
   try {
-    const [, r1, version1] = range1.match(tags)!;
-    const [, r2] = range2.match(tags)!;
+    const [, r1, version1] = range1.match(SEMVER_RANGE) ?? [];
+    const [, r2] = range2.match(SEMVER_RANGE) ?? [];
     return (
-      ['', '~', '^'].indexOf(r1) >= 0 &&
+      ['', '>=', '=', '~', '^'].includes(r1) &&
       r1 === r2 &&
       !!semver.valid(version1) &&
       semver.satisfies(version1, range2)