diff --git a/MinVer.Lib/Versioner.cs b/MinVer.Lib/Versioner.cs
index 29ca250e..921155a8 100644
--- a/MinVer.Lib/Versioner.cs
+++ b/MinVer.Lib/Versioner.cs
@@ -10,25 +10,32 @@ public static Version GetVersion(string workDir, string tagPrefix, MajorMinor mi
 
         var defaultPreReleaseIdentifiersList = defaultPreReleaseIdentifiers.ToList();
 
-        var (version, height) = GetVersion(workDir, tagPrefix, defaultPreReleaseIdentifiersList, log);
+        var (version, height, isFromTag) = GetVersion(workDir, tagPrefix, defaultPreReleaseIdentifiersList, log);
 
         _ = height.HasValue && ignoreHeight && log.IsDebugEnabled && log.Debug("Ignoring height.");
         version = !height.HasValue || ignoreHeight ? version : version.WithHeight(height.Value, autoIncrement, defaultPreReleaseIdentifiersList);
 
         version = version.AddBuildMetadata(buildMeta);
 
-        var calculatedVersion = version.Satisfying(minMajorMinor, defaultPreReleaseIdentifiersList);
+        var ignoreMinMajorMinor = isFromTag && height is 0;
 
-        _ = calculatedVersion != version
-            ? log.IsInfoEnabled && log.Info($"Bumping version to {calculatedVersion} to satisfy minimum major minor {minMajorMinor}.")
-            : log.IsDebugEnabled && log.Debug($"The calculated version {calculatedVersion} satisfies the minimum major minor {minMajorMinor}.");
+        var calculatedVersion =
+            ignoreMinMajorMinor
+            ? version.Satisfying(MajorMinor.Default, defaultPreReleaseIdentifiersList)
+            : version.Satisfying(minMajorMinor, defaultPreReleaseIdentifiersList);
+
+        _ = ignoreMinMajorMinor
+            ? minMajorMinor != MajorMinor.Default && log.IsDebugEnabled && log.Debug($"Ignoring minimum major minor {minMajorMinor} because the commit is tagged.")
+            : calculatedVersion != version
+                ? log.IsInfoEnabled && log.Info($"Bumping version to {calculatedVersion} to satisfy minimum major minor {minMajorMinor}.")
+                : log.IsDebugEnabled && log.Debug($"The calculated version {calculatedVersion} satisfies the minimum major minor {minMajorMinor}.");
 
         _ = log.IsInfoEnabled && log.Info($"Calculated version {calculatedVersion}.");
 
         return calculatedVersion;
     }
 
-    private static (Version Version, int? Height) GetVersion(string workDir, string tagPrefix, List<string> defaultPreReleaseIdentifiers, ILogger log)
+    private static (Version Version, int? Height, bool IsFromTag) GetVersion(string workDir, string tagPrefix, List<string> defaultPreReleaseIdentifiers, ILogger log)
     {
         if (!Git.IsWorkingDirectory(workDir, log))
         {
@@ -36,7 +43,7 @@ private static (Version Version, int? Height) GetVersion(string workDir, string
 
             _ = log.IsWarnEnabled && log.Warn(1001, $"'{workDir}' is not a valid Git working directory. Using default version {version}.");
 
-            return (version, default);
+            return (version, default, default);
         }
 
         if (!Git.TryGetHead(workDir, out var head, log))
@@ -45,7 +52,7 @@ private static (Version Version, int? Height) GetVersion(string workDir, string
 
             _ = log.IsInfoEnabled && log.Info($"No commits found. Using default version {version}.");
 
-            return (version, default);
+            return (version, default, default);
         }
 
         var tags = Git.GetTags(workDir, log);
@@ -71,7 +78,7 @@ private static (Version Version, int? Height) GetVersion(string workDir, string
         _ = string.IsNullOrEmpty(selectedCandidate.Tag) && log.IsInfoEnabled && log.Info($"No commit found with a valid SemVer 2.0 version{(string.IsNullOrEmpty(tagPrefix) ? "" : $" prefixed with '{tagPrefix}'")}. Using default version {selectedCandidate.Version}.");
         _ = log.IsInfoEnabled && log.Info($"Using{(log.IsDebugEnabled && orderedCandidates.Count > 1 ? "    " : " ")}{selectedCandidate.ToString(tagWidth, versionWidth, heightWidth)}.");
 
-        return (selectedCandidate.Version, selectedCandidate.Height);
+        return (selectedCandidate.Version, selectedCandidate.Height, !string.IsNullOrEmpty(selectedCandidate.Tag));
     }
 
     private static List<Candidate> GetCandidates(Commit head, IEnumerable<(string Name, string Sha)> tags, string tagPrefix, IReadOnlyCollection<string> defaultPreReleaseIdentifiers, ILogger log)
diff --git a/MinVerTests.Lib/LogMessages.cs b/MinVerTests.Lib/LogMessages.cs
index b06bdc9f..00036b98 100644
--- a/MinVerTests.Lib/LogMessages.cs
+++ b/MinVerTests.Lib/LogMessages.cs
@@ -13,7 +13,7 @@ public static class LogMessages
     [Theory]
     [InlineData(0, 0)]
     [InlineData(2, 0)]
-    public static async Task RepoWithHistory(int minMajor, int minMinor)
+    public static async Task MinimumMajorMinorAfterTag(int minMajor, int minMinor)
     {
         // arrange
         var minMajorMinor = new MajorMinor(minMajor, minMinor);
@@ -67,8 +67,52 @@ git checkout main
         _ = Versioner.GetVersion(path, "", minMajorMinor, "", default, PreReleaseIdentifiers.Default, false, log);
 
         // assert
-        var logMessages = log.ToString();
+        var logMessages = await ReplaceShas(log.ToString(), path);
 
+        await AssertFile.Contains($"../../../log.{minMajorMinor}.txt", logMessages);
+    }
+
+    [Theory]
+    [InlineData(3, 0)]
+    public static async Task MinimumMajorMinorOnTag(int minMajor, int minMinor)
+    {
+        // arrange
+        var minMajorMinor = new MajorMinor(minMajor, minMinor);
+
+        var historicalCommands =
+            @"
+git commit --allow-empty -m '.'
+git tag not-a-version
+git checkout -b foo
+git commit --allow-empty -m '.'
+git tag 1.0.0-foo.1
+";
+
+        var path = MethodBase.GetCurrentMethod().GetTestDirectory(minMajorMinor);
+
+        await EnsureEmptyRepository(path);
+
+        foreach (var item in historicalCommands
+            .ToNonEmptyLines()
+            .Select((command, index) => new { Command = command, Index = $"{index}", }))
+        {
+            var nameAndArgs = item.Command.Split(" ", 2);
+            _ = await ReadAsync(nameAndArgs[0], nameAndArgs[1], path);
+        }
+
+        var log = new TestLogger();
+
+        // act
+        _ = Versioner.GetVersion(path, "", minMajorMinor, "", default, PreReleaseIdentifiers.Default, false, log);
+
+        // assert
+        var logMessages = await ReplaceShas(log.ToString(), path);
+
+        await AssertFile.Contains($"../../../log.{minMajorMinor}.txt", logMessages);
+    }
+
+    private static async Task<string> ReplaceShas(string logMessages, string path)
+    {
         var shas = (await ReadAsync("git", "log --pretty=format:\"%H\"", path))
             .StandardOutput
             .ToNonEmptyLines()
@@ -85,6 +129,6 @@ git checkout main
             logMessages = logMessages.Replace(item.ShortSha, $"{item.Index}", StringComparison.Ordinal);
         }
 
-        await AssertFile.Contains($"../../../log.{minMajorMinor}.txt", logMessages);
+        return logMessages;
     }
 }
diff --git a/MinVerTests.Lib/MinMajorMinor.cs b/MinVerTests.Lib/MinMajorMinor.cs
index cf1ba564..56ccc60b 100644
--- a/MinVerTests.Lib/MinMajorMinor.cs
+++ b/MinVerTests.Lib/MinMajorMinor.cs
@@ -24,10 +24,10 @@ public static async Task NoCommits()
     }
 
     [Theory]
-    [InlineData("4.0.0", 3, 2, "4.0.0", true)]
-    [InlineData("4.3.0", 4, 3, "4.3.0", true)]
-    [InlineData("4.3.0", 5, 4, "5.4.0-alpha.0", false)]
-    public static async Task Tagged(string tag, int major, int minor, string expectedVersion, bool isRedundant)
+    [InlineData("4.0.0", 3, 2, "4.0.0")]
+    [InlineData("4.3.0", 4, 3, "4.3.0")]
+    [InlineData("4.3.0", 5, 4, "4.3.0")]
+    public static async Task Tagged(string tag, int major, int minor, string expectedVersion)
     {
         // arrange
         var path = MethodBase.GetCurrentMethod().GetTestDirectory((tag, major, minor));
@@ -41,10 +41,7 @@ public static async Task Tagged(string tag, int major, int minor, string expecte
         // assert
         Assert.Equal(expectedVersion, actualVersion.ToString());
 
-        if (isRedundant)
-        {
-            Assert.Contains(logger.Messages, message => message.Text.Contains($"The calculated version {actualVersion} satisfies the minimum major minor {major}.{minor}.", StringComparison.Ordinal));
-        }
+        Assert.Contains(logger.Messages, message => message.Text.Contains($"Ignoring minimum major minor {major}.{minor} because the commit is tagged.", StringComparison.Ordinal));
     }
 
     [Fact]
diff --git a/MinVerTests.Lib/log.3.0.txt b/MinVerTests.Lib/log.3.0.txt
new file mode 100644
index 00000000..17a1c6ad
--- /dev/null
+++ b/MinVerTests.Lib/log.3.0.txt
@@ -0,0 +1,32 @@
+Trace: Running Git: git status --short
+Trace: Git exit code: 0
+Trace: Git stdout:
+?? command-read-00.md
+?? command-read-01.md
+?? command-read-02.md
+?? command-read-03.md
+
+Trace: Git stderr:
+
+Trace: Running Git: git log --pretty=format:"%H %P"
+Trace: Git exit code: 0
+Trace: Git stdout:
+1 0
+0
+Trace: Git stderr:
+
+Trace: Running Git: git show-ref --tags --dereference
+Trace: Git exit code: 0
+Trace: Git stdout:
+1 refs/tags/1.0.0-foo.1
+0 refs/tags/not-a-version
+
+Trace: Git stderr:
+
+Debug: Ignoring non-version tag { Name: not-a-version, Sha: 0 }.
+Trace: Checking commit 1 (height 0)...
+Trace: Found version tag { Commit: 1, Tag: '1.0.0-foo.1', Version: 1.0.0-foo.1, Height: 0 }.
+Debug: 1 commits checked.
+Info:  Using { Commit: 1, Tag: '1.0.0-foo.1', Version: 1.0.0-foo.1, Height: 0 }.
+Debug: Ignoring minimum major minor 3.0 because the commit is tagged.
+Info:  Calculated version 1.0.0-foo.1.
diff --git a/MinVerTests.Packages/MinimumMajorMinorOnTag.cs b/MinVerTests.Packages/MinimumMajorMinorOnTag.cs
index dfdb0989..c92928e1 100644
--- a/MinVerTests.Packages/MinimumMajorMinorOnTag.cs
+++ b/MinVerTests.Packages/MinimumMajorMinorOnTag.cs
@@ -19,7 +19,7 @@ public static async Task HasMinimumMajorMinor()
 
         var envVars = ("MinVerMinimumMajorMinor".ToAltCase(), "3.0");
 
-        var expected = Package.WithVersion(3, 0, 0, ["alpha", "0",]);
+        var expected = Package.WithVersion(2, 3, 4);
 
         // act
         var (actual, _, _) = await Sdk.BuildProject(path, envVars: envVars);
diff --git a/README.md b/README.md
index dc32a64d..e32f5e49 100644
--- a/README.md
+++ b/README.md
@@ -206,6 +206,8 @@ Note that `MinVerMinimumMajorMinor` will be redundant after you create the first
 
 Also note that if the latest version tag found in the commit history has a higher `MAJOR.MINOR` than `MinVerMinimumMajorMinor`, then `MinVerMinimumMajorMinor` will be ignored.
 
+Lastly, if the the current commit has a version tag, the tag will be used as-is, even if it has a lower `MAJOR.MINOR` than `MinVerMinimumMajorMinor`.
+
 ### Can I use my own pre-release versioning scheme?
 
 Yes! MinVer doesn't care what your pre-release versioning scheme is. The default pre-release identifiers are `alpha.0`, but you can use whatever you like in your tags. If your versioning scheme is valid [SemVer 2.x](https://semver.org/spec/v2.0.0.html), it will work with MinVer.