diff --git a/doc/attr.xml b/doc/attr.xml
index ef7a8565c..5a0589f62 100644
--- a/doc/attr.xml
+++ b/doc/attr.xml
@@ -1388,7 +1388,7 @@ gap> DigraphLongestSimpleCircuit(D);
 
     For a digraph without multiple edges, a simple circuit is uniquely
     determined by its subsequence of vertices. However this is not the case for
-    a multidigraph.  The attribute <C>DigraphAllSimpleCircuits</C> ignores
+    a multidigraph.  The attribute <C>DigraphAllChordlessCycles</C> ignores
     multiple edges, and identifies a simple circuit using only its subsequence
     of vertices. See Section <Ref Subsect="DigraphAllSimpleCircuits" Style="Number" /> for more details.<P/>
 
diff --git a/gap/attr.gi b/gap/attr.gi
index 353645b8d..a42736a5f 100644
--- a/gap/attr.gi
+++ b/gap/attr.gi
@@ -1505,7 +1505,7 @@ end);
 InstallMethod(DigraphAllChordlessCycles, "for a digraph",
 [IsDigraph],
 function(D)
-  local BlockNeighbours, UnblockNeighbours, DegreeLabeling,
+  local BlockNeighbours, UnblockNeighbours,
   Triplets, CCExtension, digraph, temp, T, C, blocked, triple;
 
     if IsEmptyDigraph(D) then
@@ -1530,35 +1530,6 @@ function(D)
         return blocked;
     end;
 
-    # Computes the degree labeling
-    DegreeLabeling := function(digraph)
-        local degree, color, labeling, v, u, i, minDegree, x;
-
-        degree := List(DigraphVertices(digraph), i -> 0);
-        color := List(DigraphVertices(digraph), ReturnFalse);
-        labeling := List(DigraphVertices(digraph), i -> 0);
-        degree := List(DigraphVertices(digraph), i ->
-                            OutDegreeOfVertex(digraph, i));
-
-        for i in [1 .. DigraphNrVertices(digraph)] do
-            minDegree := DigraphNrVertices(digraph);
-            for x in DigraphVertices(digraph) do
-                if color[x] = false and degree[x] < minDegree then
-                    v := x;
-                    minDegree := degree[x];
-                fi;
-            od;
-            labeling[v] := i;
-            color[v] := true;
-            for u in OutNeighboursOfVertex(digraph, v) do
-                if color[u] = false then
-                    degree[u] := degree[u] - 1;
-                fi;
-            od;
-        od;
-        return labeling;
-    end;
-
     # Computes all possible triplets
     Triplets := function(digraph)
         local T, C, u, pair, x, y, labels;
@@ -1610,7 +1581,8 @@ function(D)
     digraph := DigraphSymmetricClosure(DigraphRemoveLoops(
                                   DigraphRemoveAllMultipleEdges(D)));
 
-    SetDigraphVertexLabels(digraph, DegreeLabeling(digraph));
+    SetDigraphVertexLabels(digraph,
+                 Reversed(DigraphDegeneracyOrdering(digraph)));
     temp := Triplets(digraph);
     T := temp[1];
     C := temp[2];
diff --git a/tst/standard/attr.tst b/tst/standard/attr.tst
index adc3896b4..35e82406d 100644
--- a/tst/standard/attr.tst
+++ b/tst/standard/attr.tst
@@ -963,9 +963,9 @@ gap> DigraphAllChordlessCycles(D);
 [ [ 2, 1, 3 ], [ 2, 1, 4 ], [ 3, 1, 4 ], [ 3, 2, 4 ] ]
 gap> D := Digraph([[2, 4, 5], [3, 6], [4, 7], [8], [6, 8], [7], [8], []]);;
 gap> DigraphAllChordlessCycles(D);
-[ [ 6, 5, 8, 7 ], [ 4, 3, 7, 8 ], [ 3, 2, 6, 5, 8, 4 ], [ 3, 2, 6, 7 ], 
-  [ 4, 1, 5, 6, 7, 3 ], [ 4, 1, 5, 8 ], [ 2, 1, 5, 6 ], [ 2, 1, 5, 8, 7, 3 ], 
-  [ 2, 1, 4, 3 ], [ 2, 1, 4, 8, 7, 6 ] ]
+[ [ 6, 5, 8, 7 ], [ 3, 4, 8, 5, 6, 2 ], [ 3, 4, 8, 7 ], [ 1, 4, 8, 5 ], 
+  [ 1, 4, 8, 7, 6, 2 ], [ 1, 4, 3, 2 ], [ 1, 4, 3, 7, 6, 5 ], [ 3, 2, 6, 7 ], 
+  [ 2, 1, 5, 6 ], [ 2, 1, 5, 8, 7, 3 ] ]
 
 #  DigraphLongestSimpleCircuit
 gap> gr := Digraph([]);;