diff --git a/tests/ImageSharp.Tests/Formats/Bmp/BmpFileHeaderTests.cs b/tests/ImageSharp.Tests/Formats/Bmp/BmpFileHeaderTests.cs
index 25cf29406..140686708 100644
--- a/tests/ImageSharp.Tests/Formats/Bmp/BmpFileHeaderTests.cs
+++ b/tests/ImageSharp.Tests/Formats/Bmp/BmpFileHeaderTests.cs
@@ -1,4 +1,10 @@
+// Copyright (c) Six Labors and contributors.
+// Licensed under the Apache License, Version 2.0.
+
 using System;
+using System.IO;
+
+using SixLabors.ImageSharp.Formats;
 using SixLabors.ImageSharp.Formats.Bmp;
 using Xunit;
 
@@ -6,6 +12,10 @@ namespace SixLabors.ImageSharp.Tests.Formats.Bmp
 {
     public class BmpFileHeaderTests
     {
+        private static readonly byte[] Data = BitConverter.GetBytes(BmpConstants.TypeMarkers.Bitmap);
+
+        private MemoryStream Stream { get; } = new MemoryStream(Data);
+
         [Fact]
         public void TestWrite()
         {
@@ -17,5 +27,16 @@ namespace SixLabors.ImageSharp.Tests.Formats.Bmp
 
             Assert.Equal("AQACAAAAAwAAAAQAAAA=", Convert.ToBase64String(buffer));
         }
+
+        [Fact]
+        public void ImageLoad_WithoutEnoughData_Throws_UnknownImageFormatException()
+        {
+            Assert.Throws<UnknownImageFormatException>(() =>
+            {
+                using (Image.Load(Configuration.Default, this.Stream, out IImageFormat _))
+                {
+                }
+            });
+        }
     }
 }
diff --git a/tests/ImageSharp.Tests/Formats/Tga/TgaFileHeaderTests.cs b/tests/ImageSharp.Tests/Formats/Tga/TgaFileHeaderTests.cs
new file mode 100644
index 000000000..943144d61
--- /dev/null
+++ b/tests/ImageSharp.Tests/Formats/Tga/TgaFileHeaderTests.cs
@@ -0,0 +1,29 @@
+// Copyright (c) Six Labors and contributors.
+// Licensed under the Apache License, Version 2.0.
+
+using System.IO;
+
+using SixLabors.ImageSharp.Formats;
+
+using Xunit;
+
+namespace SixLabors.ImageSharp.Tests.Formats.Tga
+{
+    public class TgaFileHeaderTests
+    {
+        private static readonly byte[] Data = { 0, 0, 0 };
+
+        private MemoryStream Stream { get; } = new MemoryStream(Data);
+
+        [Fact]
+        public void ImageLoad_WithoutEnoughData_Throws_UnknownImageFormatException()
+        {
+            Assert.Throws<UnknownImageFormatException>(() =>
+            {
+                using (Image.Load(Configuration.Default, this.Stream, out IImageFormat _))
+                {
+                }
+            });
+        }
+    }
+}