diff --git a/src/FibonacciHeap.cs b/src/FibonacciHeap.cs
index 646de58..8f1e76e 100644
--- a/src/FibonacciHeap.cs
+++ b/src/FibonacciHeap.cs
@@ -58,13 +58,22 @@ public void DecreaseKey(Node node, T newKey) {
             }
         }
 
+        /// <summary>
+        /// Cut the link between a node and its parent, moving the node to the root list.
+        /// </summary>
+
         private void Cut(Node node, Node parent) {
-            RemoveNodeFromList(node);
             parent.Degree--;
+            parent.Child = (node.Next == node ? null : node.Next);
+            RemoveNodeFromList(node);
             MergeLists(_minNode, node);
             node.IsMarked = false;
         }
 
+        /// <summary>
+        /// Perform a cascading cut on a node; mark the node if it is not marked, otherwise cut the
+        /// node and perform a cascading cut on its parent.
+        /// </summary>
         private void CascadingCut(Node node) {
             Node parent = node.Parent;
             if (parent != null) {
@@ -81,7 +90,6 @@ public void Delete(Node node) {
             // This is a special implementation of decreaseKey that sets the
             // argument to the minimum value. This is necessary to make generic keys
             // work, since there is no MIN_VALUE constant for generic types.
-            node.IsMinimum = true;
             Node parent = node.Parent;
             if (parent != null) {
                 Cut(node, parent);
@@ -104,7 +112,7 @@ public Node ExtractMinimum() {
                     } while (child != extractedMin.Child);
                 }
 
-                Node nextInRootList = _minNode.Next == _minNode ? null : _minNode.Next;
+                Node nextInRootList = extractedMin.Next == extractedMin ? null : extractedMin.Next;
 
                 // Remove min from root list
                 RemoveNodeFromList(extractedMin);
@@ -186,6 +194,9 @@ private void RemoveNodeFromList(Node node) {
             node.Prev = node;
         }
 
+        /// <summary>
+        /// Links two heaps of the same order together.
+        /// </summary>
         private void LinkHeaps(Node max, Node min) {
             RemoveNodeFromList(max);
             min.Child = MergeLists(max, min.Child);
@@ -236,7 +247,6 @@ public class Node : IComparable {
             public Node Prev { get; set; }
             public Node Next { get; set; }
             public bool IsMarked { get; set; } 
-            public bool IsMinimum { get; set; }
 
             public Node() {
                 Key = default(T);
diff --git a/test/FibonacciHeap/FibonacciHeapDecreaseKeyTest.cs b/test/FibonacciHeap/FibonacciHeapDecreaseKeyTest.cs
new file mode 100644
index 0000000..bdb8bbd
--- /dev/null
+++ b/test/FibonacciHeap/FibonacciHeapDecreaseKeyTest.cs
@@ -0,0 +1,129 @@
+using GrowingWithTheWeb.DataStructures;
+using Xunit;
+
+public class FibonacciHeapDecreaseKeyTest {
+    [Fact]
+    public void LeavesValidTreeOnFlatHeapTest() {
+        var heap = new FibonacciHeap<int>();
+        heap.Insert(13);
+        heap.Insert(26);
+        heap.Insert(3);
+        heap.Insert(-6);
+        heap.Insert(27);
+        var node6 = heap.Insert(88);
+        heap.Insert(59);
+        heap.Insert(-10);
+        heap.Insert(16);
+        heap.DecreaseKey(node6, -8);
+        Assert.Equal(heap.ExtractMinimum().Key, -10);
+        Assert.Equal(heap.ExtractMinimum().Key, -8);
+        Assert.Equal(heap.ExtractMinimum().Key, -6);
+        Assert.Equal(heap.ExtractMinimum().Key, 3);
+        Assert.Equal(heap.ExtractMinimum().Key, 13);
+        Assert.Equal(heap.ExtractMinimum().Key, 16);
+        Assert.Equal(heap.ExtractMinimum().Key, 26);
+        Assert.Equal(heap.ExtractMinimum().Key, 27);
+        Assert.Equal(heap.ExtractMinimum().Key, 59);
+    }
+
+    [Fact]
+    public void LeavesValidTreeOnConsolidatedHeapTest() {
+        var heap = new FibonacciHeap<int>();
+        var node0 = heap.Insert(0);
+        var node1 = heap.Insert(1);
+        var node2 = heap.Insert(2);
+        var node3 = heap.Insert(3);
+        var node4 = heap.Insert(4);
+        var node5 = heap.Insert(5);
+        var node6 = heap.Insert(6);
+        var node7 = heap.Insert(7);
+        var node8 = heap.Insert(8);
+
+        // Extracting minimum should trigger consolidate.
+        //
+        //                                    __1
+        //                                   / /|
+        //                                  5 3 2
+        //  0--1--2--3--4--5--6--7--8  ->  /| |
+        //                                7 6 4
+        //                                |
+        //                                8
+        //
+        Assert.Equal(heap.ExtractMinimum(), node0);
+
+        // Decrease node 8 to 0
+        //
+        //      __1
+        //     / /|        __1--0
+        //    5 3 2       / /|
+        //   /| |    ->  5 3 2
+        //  7 6 4       /| |
+        //  |          7 6 4
+        //  8
+        //
+        heap.DecreaseKey(node8, 0);
+        Assert.True(node1.Next == node8);
+
+        Assert.Equal(heap.Size, 8);
+        Assert.True(heap.ExtractMinimum() == node8);
+        Assert.True(heap.ExtractMinimum() == node1);
+        Assert.True(heap.ExtractMinimum() == node2);
+        Assert.True(heap.ExtractMinimum() == node3);
+        Assert.True(heap.ExtractMinimum() == node4);
+        Assert.True(heap.ExtractMinimum() == node5);
+        Assert.True(heap.ExtractMinimum() == node6);
+        Assert.True(heap.ExtractMinimum() == node7);
+        Assert.True(heap.IsEmpty());
+    }
+}
+/*
+
+test('should leave a valid tree on a consolidated Fibonacci heap', function (t) {
+  var heap = new Heap();
+  var node0 = heap.insert(0, null);
+  var node1 = heap.insert(1, null);
+  var node2 = heap.insert(2, null);
+  var node3 = heap.insert(3, null);
+  var node4 = heap.insert(4, null);
+  var node5 = heap.insert(5, null);
+  var node6 = heap.insert(6, null);
+  var node7 = heap.insert(7, null);
+  var node8 = heap.insert(8, null);
+
+  // Extracting minimum should trigger consolidate.
+  //
+  //                                    __1
+  //                                   / /|
+  //                                  5 3 2
+  //  0--1--2--3--4--5--6--7--8  ->  /| |
+  //                                7 6 4
+  //                                |
+  //                                8
+  //
+  t.is(heap.extractMinimum(), node0);
+
+  // Decrease node 8 to 0
+  //
+  //      __1
+  //     / /|        __1--0
+  //    5 3 2       / /|
+  //   /| |    ->  5 3 2
+  //  7 6 4       /| |
+  //  |          7 6 4
+  //  8
+  //
+  heap.decreaseKey(node8, 0);
+  t.true(node1.next === node8);
+
+  t.is(heap.size(), 8);
+  t.true(heap.extractMinimum() === node8);
+  t.true(heap.extractMinimum() === node1);
+  t.true(heap.extractMinimum() === node2);
+  t.true(heap.extractMinimum() === node3);
+  t.true(heap.extractMinimum() === node4);
+  t.true(heap.extractMinimum() === node5);
+  t.true(heap.extractMinimum() === node6);
+  t.true(heap.extractMinimum() === node7);
+  t.true(heap.isEmpty());
+});
+*/
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