diff --git a/src/installer.ts b/src/installer.ts
index dc1234a..d9d9555 100644
--- a/src/installer.ts
+++ b/src/installer.ts
@@ -179,7 +179,15 @@ export function getJuliaVersion(availableReleases: string[], versionInput: strin
         if (!juliaCompatRange) {
             throw new Error('Unable to use version "min" when the Julia project file does not specify a compat for Julia')
         }
-        version = semver.minSatisfying(availableReleases, juliaCompatRange, {includePrerelease})
+        // true_min_version is the actual minimum
+        // E.g. if the Julia [compat] entry is "1.10", then true_min_version is v"1.10.0"
+        let true_min_version = semver.minSatisfying(availableReleases, juliaCompatRange, {includePrerelease})
+        let my_tilde_range = `~${true_min_version}`
+        // min_with_patch is the minimum major/minor, but latest patch
+        // E.g. if the Julia [compat] entry is "1.10", then true_min_version is v"1.10.10" (or whatever the latest 1.10.x patch is)
+        // https://github.com/julia-actions/setup-julia/issues/372
+        min_with_patch = semver.maxSatisfying(availableReleases, my_tilde_range, {includePrerelease})
+        version = min_with_patch
     } else if (versionInput == "lts") {
         version = semver.maxSatisfying(availableReleases, LTS_VERSION, { includePrerelease: false });
     } else if (versionInput == "pre") {