diff --git a/src/ImageSharp/Formats/Bmp/BmpDecoderCore.cs b/src/ImageSharp/Formats/Bmp/BmpDecoderCore.cs
index 960c2ecd22..fdd371f547 100644
--- a/src/ImageSharp/Formats/Bmp/BmpDecoderCore.cs
+++ b/src/ImageSharp/Formats/Bmp/BmpDecoderCore.cs
@@ -114,6 +114,9 @@ namespace SixLabors.ImageSharp.Formats.Bmp
             this.options = options;
         }
 
+        /// <summary>
+        /// Gets the dimensions of the image.
+        /// </summary>
         public Size Dimensions => new Size(this.infoHeader.Width, this.infoHeader.Height);
 
         /// <summary>
diff --git a/src/ImageSharp/Formats/Gif/GifDecoder.cs b/src/ImageSharp/Formats/Gif/GifDecoder.cs
index 7691ec1aa5..24e3d88261 100644
--- a/src/ImageSharp/Formats/Gif/GifDecoder.cs
+++ b/src/ImageSharp/Formats/Gif/GifDecoder.cs
@@ -1,7 +1,9 @@
 // Copyright (c) Six Labors and contributors.
 // Licensed under the Apache License, Version 2.0.
 
+using System;
 using System.IO;
+using SixLabors.ImageSharp.Memory;
 using SixLabors.ImageSharp.Metadata;
 using SixLabors.ImageSharp.PixelFormats;
 
@@ -27,7 +29,19 @@ namespace SixLabors.ImageSharp.Formats.Gif
             where TPixel : struct, IPixel<TPixel>
         {
             var decoder = new GifDecoderCore(configuration, this);
-            return decoder.Decode<TPixel>(stream);
+
+            try
+            {
+                return decoder.Decode<TPixel>(stream);
+            }
+            catch (InvalidMemoryOperationException ex)
+            {
+                Size dims = decoder.Dimensions;
+
+                // TODO: use InvalidImageContentException here, if we decide to define it
+                // https://github.com/SixLabors/ImageSharp/issues/1110
+                throw new ImageFormatException($"Can not decode image. Failed to allocate buffers for possibly degenerate dimensions: {dims.Width}x{dims.Height}.", ex);
+            }
         }
 
         /// <inheritdoc/>
diff --git a/src/ImageSharp/Formats/Gif/GifDecoderCore.cs b/src/ImageSharp/Formats/Gif/GifDecoderCore.cs
index 98dbddb481..bc508cba74 100644
--- a/src/ImageSharp/Formats/Gif/GifDecoderCore.cs
+++ b/src/ImageSharp/Formats/Gif/GifDecoderCore.cs
@@ -86,10 +86,15 @@ namespace SixLabors.ImageSharp.Formats.Gif
         public bool IgnoreMetadata { get; internal set; }
 
         /// <summary>
-        /// Gets the decoding mode for multi-frame images
+        /// Gets the decoding mode for multi-frame images.
         /// </summary>
         public FrameDecodingMode DecodingMode { get; }
 
+        /// <summary>
+        /// Gets the dimensions of the image.
+        /// </summary>
+        public Size Dimensions => new Size(this.imageDescriptor.Width, this.imageDescriptor.Height);
+
         private MemoryAllocator MemoryAllocator => this.configuration.MemoryAllocator;
 
         /// <summary>
diff --git a/src/ImageSharp/Formats/Png/PngDecoderCore.cs b/src/ImageSharp/Formats/Png/PngDecoderCore.cs
index ff75e4290f..2701bd2a74 100644
--- a/src/ImageSharp/Formats/Png/PngDecoderCore.cs
+++ b/src/ImageSharp/Formats/Png/PngDecoderCore.cs
@@ -132,6 +132,9 @@ namespace SixLabors.ImageSharp.Formats.Png
             this.ignoreMetadata = options.IgnoreMetadata;
         }
 
+        /// <summary>
+        /// Gets the dimensions of the image.
+        /// </summary>
         public Size Dimensions => new Size(this.header.Width, this.header.Height);
 
         /// <summary>
diff --git a/src/ImageSharp/Formats/Tga/TgaDecoderCore.cs b/src/ImageSharp/Formats/Tga/TgaDecoderCore.cs
index 1717df63b6..6768f4db30 100644
--- a/src/ImageSharp/Formats/Tga/TgaDecoderCore.cs
+++ b/src/ImageSharp/Formats/Tga/TgaDecoderCore.cs
@@ -61,6 +61,9 @@ namespace SixLabors.ImageSharp.Formats.Tga
             this.options = options;
         }
 
+        /// <summary>
+        /// Gets the dimensions of the image.
+        /// </summary>
         public Size Dimensions => new Size(this.fileHeader.Width, this.fileHeader.Height);
 
         /// <summary>
diff --git a/tests/ImageSharp.Tests/Formats/Gif/GifDecoderTests.cs b/tests/ImageSharp.Tests/Formats/Gif/GifDecoderTests.cs
index 99dc2d06da..ea244f68ab 100644
--- a/tests/ImageSharp.Tests/Formats/Gif/GifDecoderTests.cs
+++ b/tests/ImageSharp.Tests/Formats/Gif/GifDecoderTests.cs
@@ -4,10 +4,14 @@
 using System;
 using System.Collections.Generic;
 using System.IO;
+using Microsoft.DotNet.RemoteExecutor;
 using SixLabors.ImageSharp.Advanced;
 using SixLabors.ImageSharp.Formats.Gif;
+using SixLabors.ImageSharp.Formats.Tga;
+using SixLabors.ImageSharp.Memory;
 using SixLabors.ImageSharp.Metadata;
 using SixLabors.ImageSharp.PixelFormats;
+using SixLabors.ImageSharp.Tests.TestUtilities;
 using SixLabors.ImageSharp.Tests.TestUtilities.ImageComparison;
 using Xunit;
 
@@ -163,5 +167,41 @@ namespace SixLabors.ImageSharp.Tests.Formats.Gif
                 }
             }
         }
+
+        [Theory]
+        [WithFile(TestImages.Gif.Giphy, PixelTypes.Rgba32)]
+        [WithFile(TestImages.Gif.Kumin, PixelTypes.Rgba32)]
+        public void GifDecoder_DegenerateMemoryRequest_ShouldTranslateTo_ImageFormatException<TPixel>(TestImageProvider<TPixel> provider)
+            where TPixel : struct, IPixel<TPixel>
+        {
+            provider.LimitAllocatorBufferCapacity().InPixels(10);
+            ImageFormatException ex = Assert.Throws<ImageFormatException>(provider.GetImage);
+            Assert.IsType<InvalidMemoryOperationException>(ex.InnerException);
+        }
+
+        [Theory]
+        [WithFile(TestImages.Gif.Giphy, PixelTypes.Rgba32)]
+        [WithFile(TestImages.Gif.Kumin, PixelTypes.Rgba32)]
+        public void GifDecoder_CanDecode_WithLimitedAllocatorBufferCapacity<TPixel>(TestImageProvider<TPixel> provider)
+            where TPixel : struct, IPixel<TPixel>
+        {
+            static void RunTest(string providerDump, string nonContiguousBuffersStr)
+            {
+                TestImageProvider<TPixel> provider = BasicSerializer.Deserialize<TestImageProvider<TPixel>>(providerDump);
+
+                provider.LimitAllocatorBufferCapacity().InPixels(100);
+
+                using Image<TPixel> image = provider.GetImage(new GifDecoder());
+                image.DebugSave(provider);
+                image.CompareToOriginal(provider);
+            }
+
+            string providerDump = BasicSerializer.Serialize(provider);
+            RemoteExecutor.Invoke(
+                    RunTest,
+                    providerDump,
+                    "Disco")
+                .Dispose();
+        }
     }
 }
diff --git a/tests/ImageSharp.Tests/Formats/Gif/GifEncoderTests.cs b/tests/ImageSharp.Tests/Formats/Gif/GifEncoderTests.cs
index fe1faa5aed..4c710cdb2e 100644
--- a/tests/ImageSharp.Tests/Formats/Gif/GifEncoderTests.cs
+++ b/tests/ImageSharp.Tests/Formats/Gif/GifEncoderTests.cs
@@ -26,10 +26,16 @@ namespace SixLabors.ImageSharp.Tests.Formats.Gif
         };
 
         [Theory]
-        [WithTestPatternImages(100, 100, TestPixelTypes)]
-        public void EncodeGeneratedPatterns<TPixel>(TestImageProvider<TPixel> provider)
+        [WithTestPatternImages(100, 100, TestPixelTypes, false)]
+        [WithTestPatternImages(100, 100, TestPixelTypes, false)]
+        public void EncodeGeneratedPatterns<TPixel>(TestImageProvider<TPixel> provider, bool limitAllocationBuffer)
             where TPixel : struct, IPixel<TPixel>
         {
+            if (limitAllocationBuffer)
+            {
+                provider.LimitAllocatorBufferCapacity().InPixels(100);
+            }
+
             using (Image<TPixel> image = provider.GetImage())
             {
                 var encoder = new GifEncoder