diff --git a/src/Avalonia.Base/Data/BindingOperations.cs b/src/Avalonia.Base/Data/BindingOperations.cs
index 15de6c4d0d..44b47329ac 100644
--- a/src/Avalonia.Base/Data/BindingOperations.cs
+++ b/src/Avalonia.Base/Data/BindingOperations.cs
@@ -10,6 +10,8 @@ namespace Avalonia.Data
 {
     public static class BindingOperations
     {
+        public static readonly object DoNothing = new object();
+
         /// <summary>
         /// Applies an <see cref="InstancedBinding"/> a property on an <see cref="IAvaloniaObject"/>.
         /// </summary>
diff --git a/src/Avalonia.Base/Data/Core/BindingExpression.cs b/src/Avalonia.Base/Data/Core/BindingExpression.cs
index f1717bde3b..7f8396cdfa 100644
--- a/src/Avalonia.Base/Data/Core/BindingExpression.cs
+++ b/src/Avalonia.Base/Data/Core/BindingExpression.cs
@@ -114,6 +114,11 @@ namespace Avalonia.Data.Core
         /// <inheritdoc/>
         public void OnNext(object value)
         {
+            if (value == BindingOperations.DoNothing)
+            {
+                return;
+            }
+
             using (_inner.Subscribe(_ => { }))
             {
                 var type = _inner.ResultType;
@@ -126,6 +131,11 @@ namespace Avalonia.Data.Core
                         ConverterParameter,
                         CultureInfo.CurrentCulture);
 
+                    if (converted == BindingOperations.DoNothing)
+                    {
+                        return;
+                    }
+
                     if (converted == AvaloniaProperty.UnsetValue)
                     {
                         converted = TypeUtilities.Default(type);
@@ -186,6 +196,11 @@ namespace Avalonia.Data.Core
         /// <inheritdoc/>
         private object ConvertValue(object value)
         {
+            if (value == BindingOperations.DoNothing)
+            {
+                return value;
+            }
+
             var notification = value as BindingNotification;
 
             if (notification == null)
@@ -196,6 +211,11 @@ namespace Avalonia.Data.Core
                     ConverterParameter,
                     CultureInfo.CurrentCulture);
 
+                if (converted == BindingOperations.DoNothing)
+                {
+                    return converted;
+                }
+
                 notification = converted as BindingNotification;
 
                 if (notification?.ErrorType == BindingErrorType.None)
@@ -327,7 +347,18 @@ namespace Avalonia.Data.Core
 
             public void OnNext(object value)
             {
+                if (value == BindingOperations.DoNothing)
+                {
+                    return;
+                }
+
                 var converted = _owner.ConvertValue(value);
+
+                if (converted == BindingOperations.DoNothing)
+                {
+                    return;
+                }
+
                 _owner._value = new WeakReference<object>(converted);
                 _owner.PublishNext(converted);
             }
diff --git a/src/Markup/Avalonia.Markup/Data/MultiBinding.cs b/src/Markup/Avalonia.Markup/Data/MultiBinding.cs
index 33d12e8eb5..19f92149ec 100644
--- a/src/Markup/Avalonia.Markup/Data/MultiBinding.cs
+++ b/src/Markup/Avalonia.Markup/Data/MultiBinding.cs
@@ -97,7 +97,12 @@ namespace Avalonia.Data
             var culture = CultureInfo.CurrentCulture;
             var converted = converter.Convert(values, targetType, ConverterParameter, culture);
 
-            if (converted == AvaloniaProperty.UnsetValue && FallbackValue != null)
+            if (converted == BindingOperations.DoNothing)
+            {
+                return converted;
+            }
+
+            if (converted == AvaloniaProperty.UnsetValue)
             {
                 converted = FallbackValue;
             }
diff --git a/tests/Avalonia.Markup.Xaml.UnitTests/Converters/ValueConverterTests.cs b/tests/Avalonia.Markup.Xaml.UnitTests/Converters/ValueConverterTests.cs
new file mode 100644
index 0000000000..6f2c4363e2
--- /dev/null
+++ b/tests/Avalonia.Markup.Xaml.UnitTests/Converters/ValueConverterTests.cs
@@ -0,0 +1,71 @@
+using System;
+using System.Globalization;
+using Avalonia.Controls;
+using Avalonia.Data;
+using Avalonia.Data.Converters;
+using Avalonia.UnitTests;
+using Xunit;
+
+namespace Avalonia.Markup.Xaml.UnitTests.Converters
+{
+    public class ValueConverterTests
+    {
+        [Fact]
+        public void ValueConverter_Special_Values_Work()
+        {
+            using (UnitTestApplication.Start(TestServices.StyledWindow))
+            {
+                var xaml = @"
+<Window xmlns='https://github.com/avaloniaui'
+        xmlns:x='http://schemas.microsoft.com/winfx/2006/xaml'
+        xmlns:c='clr-namespace:Avalonia.Markup.Xaml.UnitTests.Converters;assembly=Avalonia.Markup.Xaml.UnitTests'>
+    <TextBlock Name='textBlock' Text='{Binding Converter={x:Static c:TestConverter.Instance}, FallbackValue=bar}'/>
+</Window>";
+                var loader = new AvaloniaXamlLoader();
+                var window = (Window)loader.Load(xaml);
+                var textBlock = window.FindControl<TextBlock>("textBlock");
+
+                window.ApplyTemplate();
+
+                window.DataContext = 2;
+                Assert.Equal("foo", textBlock.Text);
+
+                window.DataContext = -3;
+                Assert.Equal("foo", textBlock.Text);
+
+                window.DataContext = 0;
+                Assert.Equal("bar", textBlock.Text);
+            }
+        }
+    }
+
+    public class TestConverter : IValueConverter
+    {
+        public static readonly TestConverter Instance = new TestConverter();
+
+        public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
+        {
+            if (value is int i)
+            {
+                if (i > 0)
+                {
+                    return "foo";
+                }
+
+                if (i == 0)
+                {
+                    return AvaloniaProperty.UnsetValue;
+                }
+
+                return BindingOperations.DoNothing;
+            }
+
+            return "(default)";
+        }
+
+        public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
+        {
+            throw new NotImplementedException();
+        }
+    }
+}
diff --git a/tests/Avalonia.Markup.Xaml.UnitTests/Data/BindingTests.cs b/tests/Avalonia.Markup.Xaml.UnitTests/Data/BindingTests.cs
index 0a00b9d39d..e412657711 100644
--- a/tests/Avalonia.Markup.Xaml.UnitTests/Data/BindingTests.cs
+++ b/tests/Avalonia.Markup.Xaml.UnitTests/Data/BindingTests.cs
@@ -1,20 +1,10 @@
 // Copyright (c) The Avalonia Project. All rights reserved.
 // Licensed under the MIT license. See licence.md file in the project root for full license information.
 
-using System;
-using System.Collections.Generic;
-using System.Linq;
-using System.Reactive.Linq;
 using Avalonia.Controls;
 using Avalonia.Data;
-using Avalonia.Markup.Data;
-using Moq;
-using Xunit;
-using System.ComponentModel;
-using System.Runtime.CompilerServices;
 using Avalonia.UnitTests;
-using Avalonia.Data.Converters;
-using Avalonia.Data.Core;
+using Xunit;
 
 namespace Avalonia.Markup.Xaml.UnitTests.Data
 {
@@ -40,5 +30,32 @@ namespace Avalonia.Markup.Xaml.UnitTests.Data
                 Assert.Equal("foo", textBlock.Text);
             }
         }
+
+        [Fact]
+        public void Binding_To_DoNothing_Works()
+        {
+            using (UnitTestApplication.Start(TestServices.StyledWindow))
+            {
+                var xaml = @"
+<Window xmlns='https://github.com/avaloniaui'
+        xmlns:x='http://schemas.microsoft.com/winfx/2006/xaml'>
+    <TextBlock Name='textBlock' Text='{Binding}'/>
+</Window>";
+                var loader = new AvaloniaXamlLoader();
+                var window = (Window)loader.Load(xaml);
+                var textBlock = window.FindControl<TextBlock>("textBlock");
+
+                window.ApplyTemplate();
+
+                window.DataContext = "foo";
+                Assert.Equal("foo", textBlock.Text);
+
+                window.DataContext = BindingOperations.DoNothing;
+                Assert.Equal("foo", textBlock.Text);
+
+                window.DataContext = "bar";
+                Assert.Equal("bar", textBlock.Text);
+            }
+        }
     }
 }