diff --git a/RunningStatistics.Tests/CountMap/TestCountMap.cs b/RunningStatistics.Tests/CountMap/TestCountMap.cs
index c7fc5e3..5db8950 100644
--- a/RunningStatistics.Tests/CountMap/TestCountMap.cs
+++ b/RunningStatistics.Tests/CountMap/TestCountMap.cs
@@ -1,8 +1,161 @@
 using System;
+using System.Collections.Generic;
+using Xunit;
 
 namespace RunningStatistics.Tests.CountMap;
 
 public partial class TestCountMap()
     : AbstractRunningStatsTest<int, CountMap<int>>(
-        () => Random.Shared.Next(0, 100), 
-        () => new CountMap<int>());
\ No newline at end of file
+        () => Random.Shared.Next(0, 100),
+        () => new CountMap<int>())
+{
+    [Fact]
+    public void MinKey_ThrowsIfEmpty()
+    {
+        var countMap = new CountMap<int>();
+        Assert.Throws<KeyNotFoundException>(() => countMap.MinKey());
+    }
+
+    [Fact]
+    public void MaxKey_ThrowsIfEmpty()
+    {
+        var countMap = new CountMap<int>();
+        Assert.Throws<KeyNotFoundException>(() => countMap.MaxKey());
+    }
+    
+    [Fact]
+    public void MinKey_ThrowsIfObservationIsNotComparable()
+    {
+        var countMap = new CountMap<object>();
+        countMap.Fit(new object(), 1);
+        countMap.Fit(new object(), 2);
+        Assert.Throws<ArgumentException>(() => countMap.MinKey());
+    }
+
+    [Fact]
+    public void MaxKey_ThrowsIfObservationIsNotComparable()
+    {
+        var countMap = new CountMap<object>();
+        countMap.Fit(new object(), 1);
+        countMap.Fit(new object(), 2);
+        Assert.Throws<ArgumentException>(() => countMap.MaxKey());
+    }
+    
+    [Fact]
+    public void MinKey_ReturnsMinimumKeyForNumerics()
+    {
+        var countMap = new CountMap<int>();
+        countMap.Fit(1, 2);
+        countMap.Fit(2, 3);
+        countMap.Fit(3, 1);
+
+        Assert.Equal(1, countMap.MinKey());
+    }
+
+    [Fact]
+    public void MaxKey_ReturnsMaximumKeyForNumerics()
+    {
+        var countMap = new CountMap<int>();
+        countMap.Fit(1, 2);
+        countMap.Fit(2, 3);
+        countMap.Fit(3, 1);
+
+        Assert.Equal(3, countMap.MaxKey());
+    }
+    
+    [Fact]
+    public void MinKey_ReturnsMinimumKeyForStrings()
+    {
+        var countMap = new CountMap<string>();
+        countMap.Fit("a", 2);
+        countMap.Fit("b", 3);
+        countMap.Fit("c", 1);
+
+        Assert.Equal("a", countMap.MinKey());
+    }
+
+    [Fact]
+    public void MaxKey_ReturnsMaximumKeyForStrings()
+    {
+        var countMap = new CountMap<string>();
+        countMap.Fit("a", 2);
+        countMap.Fit("b", 3);
+        countMap.Fit("c", 1);
+
+        Assert.Equal("c", countMap.MaxKey());
+    }
+    
+    [Fact]
+    public void MinKey_UsesCustomComparer()
+    {
+        var comparer = Comparer<int>.Create((x, y) => Comparer<int>.Default.Compare(-x, -y));
+        var countMap = new CountMap<int>();
+        countMap.Fit(1, 2);
+        countMap.Fit(2, 3);
+        countMap.Fit(3, 1);
+        Assert.Equal(3, countMap.MinKey(comparer));
+    }
+
+    [Fact]
+    public void MaxKey_UsesCustomComparer()
+    {
+        var comparer = Comparer<int>.Create((x, y) => Comparer<int>.Default.Compare(-x, -y));
+        var countMap = new CountMap<int>();
+        countMap.Fit(1, 2);
+        countMap.Fit(2, 3);
+        countMap.Fit(3, 1);
+        Assert.Equal(1, countMap.MaxKey(comparer));
+    }
+    
+    [Fact]
+    public void CountMap_WithCustomComparer_MinKey_ReturnsCorrectValue()
+    {
+        var comparer = Comparer<int>.Create((x, y) => Comparer<int>.Default.Compare(-x, -y));
+        var countMap = new CountMap<int>(comparer);
+        
+        countMap.Fit(1, 2);
+        countMap.Fit(2, 3);
+        countMap.Fit(3, 1);
+        
+        Assert.Equal(3, countMap.MinKey());
+    }
+    
+    [Fact]
+    public void CountMap_WithCustomComparer_MaxKey_ReturnsCorrectValue()
+    {
+        var comparer = Comparer<int>.Create((x, y) => Comparer<int>.Default.Compare(-x, -y));
+        var countMap = new CountMap<int>(comparer);
+        
+        countMap.Fit(1, 2);
+        countMap.Fit(2, 3);
+        countMap.Fit(3, 1);
+        
+        Assert.Equal(1, countMap.MaxKey());
+    }
+    
+    [Fact]
+    public void CountMap_MinKey_NullComparer_UsesDefaultComparer()
+    {
+        var comparer = Comparer<int>.Create((x, y) => Comparer<int>.Default.Compare(-x, -y));
+        var countMap = new CountMap<int>(comparer);
+        
+        countMap.Fit(1, 2);
+        countMap.Fit(2, 3);
+        countMap.Fit(3, 1);
+        
+        Assert.Equal(1, countMap.MinKey(null));
+    }
+
+    [Fact]
+    public void CountMap_MaxKey_NullComparer_UsesDefaultComparer()
+    {
+        var comparer = Comparer<int>.Create((x, y) => Comparer<int>.Default.Compare(-x, -y));
+        var countMap = new CountMap<int>(comparer);
+        
+        countMap.Fit(1, 2);
+        countMap.Fit(2, 3);
+        countMap.Fit(3, 1);
+        
+        Assert.Equal(3, countMap.MaxKey(null));
+    }
+}
\ No newline at end of file
diff --git a/RunningStatistics.Tests/CountMap/TestCountMap_Extensions.cs b/RunningStatistics.Tests/CountMap/TestCountMap_Extensions.cs
index 6163cb8..e8025a0 100644
--- a/RunningStatistics.Tests/CountMap/TestCountMap_Extensions.cs
+++ b/RunningStatistics.Tests/CountMap/TestCountMap_Extensions.cs
@@ -4,50 +4,6 @@ namespace RunningStatistics.Tests.CountMap;
 
 public partial class TestCountMap
 {
-    [Fact]
-    public void MinKey_ReturnsMinimumKeyForNumerics()
-    {
-        var countMap = new CountMap<int>();
-        countMap.Fit(1, 2);
-        countMap.Fit(2, 3);
-        countMap.Fit(3, 1);
-
-        Assert.Equal(1, countMap.MinKey());
-    }
-
-    [Fact]
-    public void MaxKey_ReturnsMaximumKeyForNumerics()
-    {
-        var countMap = new CountMap<int>();
-        countMap.Fit(1, 2);
-        countMap.Fit(2, 3);
-        countMap.Fit(3, 1);
-
-        Assert.Equal(3, countMap.MaxKey());
-    }
-    
-    [Fact]
-    public void MinKey_ReturnsMinimumKeyForStrings()
-    {
-        var countMap = new CountMap<string>();
-        countMap.Fit("a", 2);
-        countMap.Fit("b", 3);
-        countMap.Fit("c", 1);
-
-        Assert.Equal("a", countMap.MinKey());
-    }
-
-    [Fact]
-    public void MaxKey_ReturnsMaximumKeyForStrings()
-    {
-        var countMap = new CountMap<string>();
-        countMap.Fit("a", 2);
-        countMap.Fit("b", 3);
-        countMap.Fit("c", 1);
-
-        Assert.Equal("c", countMap.MaxKey());
-    }
-
     [Fact]
     public void Sum_ReturnsCorrectSum()
     {
diff --git a/RunningStatistics/Extensions/CountMapExtensions.cs b/RunningStatistics/Extensions/CountMapExtensions.cs
index 3bb1409..da3d38e 100644
--- a/RunningStatistics/Extensions/CountMapExtensions.cs
+++ b/RunningStatistics/Extensions/CountMapExtensions.cs
@@ -1,4 +1,5 @@
 using System;
+using System.Collections.Generic;
 using System.Linq;
 // ReSharper disable MemberCanBePrivate.Global
 
@@ -10,24 +11,6 @@ namespace RunningStatistics;
 
 public static class CountMapExtensions
 {
-    /// <summary>
-    /// Find the minimum key in a CountMap.
-    /// </summary>
-    public static T MinKey<T>(this CountMap<T> countMap) where T : notnull
-    {
-        var minKey = countMap.Keys.Min();
-        return minKey ?? throw new NullReferenceException();
-    }
-    
-    /// <summary>
-    /// Find the maximum key in a CountMap.
-    /// </summary>
-    public static T MaxKey<T>(this CountMap<T> countMap) where T : notnull
-    {
-        var maxKey = countMap.Keys.Max();
-        return maxKey ?? throw new NullReferenceException();
-    }
-    
     /// <summary>
     /// Find the sum of all observations in a CountMap of integers.
     /// </summary>
diff --git a/RunningStatistics/Statistics/CountMap.cs b/RunningStatistics/Statistics/CountMap.cs
index 117aa5f..efbf772 100644
--- a/RunningStatistics/Statistics/CountMap.cs
+++ b/RunningStatistics/Statistics/CountMap.cs
@@ -17,6 +17,25 @@ public sealed class CountMap<TObs> : RunningStatisticBase<TObs, CountMap<TObs>>,
 {
     private readonly Dictionary<TObs, long> _dict = new();
     private long _nobs;
+
+
+    /// <summary>
+    /// Creates a CountMap object with the default observation comparer.
+    /// </summary>
+    public CountMap()
+    {
+        // leave Comparer as null to indicate default comparer is to be used,
+        // or to indicate that no ordering is possible
+        Comparer = null;
+    }
+
+    /// <summary>
+    /// Creates a CountMap object with the given observation comparer.
+    /// </summary>
+    public CountMap(IComparer<TObs>? comparer)
+    {
+        Comparer = comparer;
+    }
     
     
     /// <summary>
@@ -42,7 +61,12 @@ public sealed class CountMap<TObs> : RunningStatisticBase<TObs, CountMap<TObs>>,
     /// </summary>
     public IEnumerable<long> Values => _dict.Values;
 
+    /// <summary>
+    /// Gets the value comparer used for ordering observations.
+    /// </summary>
+    public IComparer<TObs>? Comparer { get; }
 
+    
     protected override long GetNobs() => _nobs;
     
     public override void Fit(TObs value, long count)
@@ -85,6 +109,86 @@ public override void Reset()
     public bool ContainsKey(TObs key) => _dict.ContainsKey(key);
     
     public bool TryGetValue(TObs key, out long value) => _dict.TryGetValue(key, out value);
+
+    /// <summary>
+    /// Finds the minimum key in the count map.
+    /// </summary>
+    /// <param name="comparer">The comparer to use for finding the minimum key.
+    /// If null, the default comparer is used.</param>
+    /// <returns>The minimum key in the count map, if any exist.</returns>
+    /// <exception cref="KeyNotFoundException">
+    /// Thrown if the count map is empty and no minimum key exists.
+    /// </exception>
+    public TObs MinKey(IComparer<TObs>? comparer)
+    {
+        comparer ??= Comparer<TObs>.Default;
+
+        using var enumerator = _dict.Keys.GetEnumerator();
+        if (!enumerator.MoveNext())
+        {
+            throw new KeyNotFoundException("The minimum key does not exist.");
+        }
+
+        var min = enumerator.Current;
+        while (enumerator.MoveNext())
+        {
+            if (comparer.Compare(enumerator.Current, min) < 0)
+            {
+                min = enumerator.Current;
+            }
+        }
+
+        return min!;
+    }
+    
+    /// <summary>
+    /// Finds the minimum key in the count map.
+    /// </summary>
+    /// <returns>The minimum key in the count map, if any exist.</returns>
+    /// <exception cref="KeyNotFoundException">
+    /// Thrown if the count map is empty and no minimum key exists.
+    /// </exception>
+    public TObs MinKey() => MinKey(Comparer);
+    
+    /// <summary>
+    /// Finds the maximum key in the count map.
+    /// </summary>
+    /// <param name="comparer">The comparer to use for finding the maximum key.
+    /// If null, the default comparer is used.</param>
+    /// <returns>The maximum key in the count map, if any exist.</returns>
+    /// <exception cref="KeyNotFoundException">
+    /// Thrown if the count map is empty and no maximum key exists.
+    /// </exception>
+    public TObs MaxKey(IComparer<TObs>? comparer)
+    {
+        comparer ??= Comparer<TObs>.Default;
+        
+        using var enumerator = _dict.Keys.GetEnumerator();
+        if (!enumerator.MoveNext())
+        {
+            throw new KeyNotFoundException("The maximum key does not exist.");
+        }
+        
+        var max = enumerator.Current;
+        while (enumerator.MoveNext())
+        {
+            if (comparer.Compare(enumerator.Current, max) > 0)
+            {
+                max = enumerator.Current;
+            }
+        }
+        
+        return max!;
+    }
+    
+    /// <summary>
+    /// Finds the maximum key in the count map.
+    /// </summary>
+    /// <returns>The maximum key in the count map, if any exist.</returns>
+    /// <exception cref="KeyNotFoundException">
+    /// Thrown if the count map is empty and no maximum key exists.
+    /// </exception>
+    public TObs MaxKey() => MaxKey(Comparer);
     
     public IEnumerator<KeyValuePair<TObs, long>> GetEnumerator() => _dict.GetEnumerator();