diff --git a/gap/io.gi b/gap/io.gi
index e29ba45f8..90d7caa80 100644
--- a/gap/io.gi
+++ b/gap/io.gi
@@ -2222,11 +2222,13 @@ InstallMethod(Graph6String, "for a digraph by out-neighbours",
 [IsDigraphByOutNeighboursRep],
 function(D)
   local list, adj, n, lenlist, tablen, blist, i, j, pos, block;
-  if (IsMultiDigraph(D) or not IsSymmetricDigraph(D)
-      or DigraphHasLoops(D)) then
-    ErrorNoReturn("the argument <D> must be a symmetric digraph ",
-                  "with no loops or multiple edges,");
-  fi;
+  if IsMultiDigraph(D) then
+    ErrorNoReturn("the argument <D> must not have multiple edges; consider encoding in Disparse6 or Digraph6");
+elif not IsSymmetricDigraph(D) then
+    ErrorNoReturn("the argument <D> must be a symmetric digraph; consider encoding in Sparse6 or Disparse6");
+elif DigraphHasLoops(D) then
+    ErrorNoReturn("the argument <D> must not have loops; consider encoding in Sparse6 or Disparse6");
+fi;
 
   list := [];
   adj := OutNeighbours(D);
@@ -2285,6 +2287,15 @@ function(D)
   adj := OutNeighbours(D);
   n := Length(DigraphVertices(D));
 
+  if IsMultiDigraph(D) then
+    if IsSymmetricDigraph(D) then
+      ErrorNoReturn("the argument <D> must not have multiple edges ",
+                  "consider encoding in Sparse6 or Disparse6, ");
+    fi;
+    ErrorNoReturn("the argument <D> must not have multiple edges ",
+                  "consider encoding in Disparse6, ");
+  fi;
+
   # First write the special character '&'
   Add(list, -25);
 
@@ -2337,8 +2348,13 @@ InstallMethod(Sparse6String, "for a digraph by out-neighbours",
 function(D)
   local list, n, lenlist, adj, nredges, k, blist, v, nextbit, i, j,
         bitstopad, pos, block;
+
   if not IsSymmetricDigraph(D) then
-    ErrorNoReturn("the argument <D> must be a symmetric digraph,");
+    if IsMultiDigraph(D) then
+        ErrorNoReturn("the argument <D> must be a symmetric digraph consider encoding in Disparse6,");
+    else
+        ErrorNoReturn("the argument <D> must be a symmetric digraph consider encoding in Digraph6 or Disparse6,");
+    fi;
   fi;
 
   list := [];
diff --git a/tst/standard/io.tst b/tst/standard/io.tst
index 5c606a349..23be86e20 100644
--- a/tst/standard/io.tst
+++ b/tst/standard/io.tst
@@ -283,8 +283,8 @@ true
 gap> gr[3] := Digraph([[1, 2], [1, 2]]);
 <immutable digraph with 2 vertices, 4 edges>
 gap> WriteDigraphs(filename, Digraph([[2], []]), Graph6String);
-Error, the argument <D> must be a symmetric digraph with no loops or multiple \
-edges,
+Error, the argument <D> must be a symmetric digraph; consider encoding in Spar\
+se6 or Disparse6
 gap> OnBreak := oldOnBreak;;
 gap> IO_Close(IO.OpenFiles[Length(IO.OpenFiles)]);;
 gap> filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/test.s6.bz2");;
@@ -320,8 +320,8 @@ gap> ReadDigraphs(f);
 gap> IO_Close(f);;
 gap> f := DigraphFile(filename, "a");;
 gap> WriteDigraphs(f, CycleDigraph(5));
-Error, the argument <D> must be a symmetric digraph with no loops or multiple \
-edges,
+Error, the argument <D> must be a symmetric digraph; consider encoding in Spar\
+se6 or Disparse6
 gap> WriteDigraphs(f, JohnsonDigraph(6, 3));
 IO_OK
 gap> IO_Close(f);;
@@ -546,7 +546,8 @@ Error, the 2nd argument <s> is not a valid disparse6 string,
 
 #  Special format characters
 gap> Sparse6String(ChainDigraph(3));
-Error, the argument <D> must be a symmetric digraph,
+Error, the argument <D> must be a symmetric digraph consider encoding in Digra\
+ph6 or Disparse6,
 gap> Sparse6String(CompleteDigraph(1));
 ":@"
 gap> gr := Digraph([[1], []]);;
@@ -659,8 +660,8 @@ Error, cannot open the file given as the 1st argument <name>,
 
 #  DigraphPlainTextLineDecoder: bad input
 gap> Graph6String(ChainDigraph(4));
-Error, the argument <D> must be a symmetric digraph with no loops or multiple \
-edges,
+Error, the argument <D> must be a symmetric digraph; consider encoding in Spar\
+se6 or Disparse6
 gap> DIGRAPHS_Graph6Length(-1);
 fail
 gap> DIGRAPHS_Graph6Length(68719476737);