diff --git a/lib/ctblpope.gi b/lib/ctblpope.gi
index 0730dfa9e8..c751c1ab32 100644
--- a/lib/ctblpope.gi
+++ b/lib/ctblpope.gi
@@ -1599,7 +1599,7 @@ end );
 #############################################################################
 ##
 #F  PermCandidatesFaithful( <tbl>, <chars>, <norm\_subgrp>, <nonfaithful>,
-#F                           <lower>, <upper>, <torso> )'
+#F                           <lower>, <upper>, <torso>[, <all>] )
 ##
 # `PermCandidatesFaithful'\\
 # `      ( tbl, chars, norm\_subgrp, nonfaithful, lower, upper, torso )'
@@ -1815,9 +1815,10 @@ end );
 # `evaluate', but for `erase' it is global (realized as `[ rest ]').
 ##
 InstallGlobalFunction( PermCandidatesFaithful,
-    function( tbl, chars, norm_subgrp, nonfaithful, upper, lower, torso )
-
-    local tbl_classes,       # attribute of `tbl'
+    function( tbl, chars, norm_subgrp, nonfaithful, upper, lower, torso,
+              arg... )
+    local ratirr,
+          tbl_classes,       # attribute of `tbl'
           tbl_size,          # attribute of `tbl'
           tbl_orders,        # attribute of `tbl'
           tbl_centralizers,  # attribute of `tbl'
@@ -1831,6 +1832,15 @@ InstallGlobalFunction( PermCandidatesFaithful,
           min_class, evaluate, step, first, descendclass, oldrows, newmatrix,
           row;
 
+    chars:= List( chars, ValuesOfClassFunction );
+    if Length( arg ) = 1 and arg[1] = true then
+      # The given list contains all rational irreducible characters.
+      ratirr:= chars;
+    else
+      # The given list is not known to be complete.
+      ratirr:= RationalizedMat( List( Irr( tbl ), ValuesOfClassFunction ) );
+    fi;
+
     #
     # step 1: Try to improve the input data
     #
@@ -2109,7 +2119,7 @@ InstallGlobalFunction( PermCandidatesFaithful,
       local cand;
       cand:= List( [ 1 .. Length( gencharacter ) ],
                    i -> gencharacter[i] * tbl_classes[i] );
-      return ForAll( chars, chi -> 0 <= cand * chi );
+      return ForAll( ratirr, chi -> 0 <= cand * chi );
     end;
     #
     # and a bigger function:
@@ -2469,7 +2479,8 @@ InstallGlobalFunction( PermChars, function( arg )
         lower:= 0;
       fi;
       return PermCandidatesFaithful( tbl, chars, arec.normalsubgroup,
-            arec.nonfaithful, upper, lower, arec.torso);
+                 arec.nonfaithful, upper, lower, arec.torso,
+                 not "chars" in names );
 
    elif "torso" in names then
 
diff --git a/tst/testextra/ctblpope.tst b/tst/testextra/ctblpope.tst
new file mode 100644
index 0000000000..a74453af15
--- /dev/null
+++ b/tst/testextra/ctblpope.tst
@@ -0,0 +1,64 @@
+#############################################################################
+##
+#W  ctblpope.tst                GAP tests                       Thomas Breuer
+##
+#Y  Copyright (C) 2017
+##
+##  excluded from 'testinstall.g' as it takes considerable time
+##
+
+gap> START_TEST( "ctblpope.tst" );
+
+##
+gap> if IsPackageMarkedForLoading( "ctbllib", "" ) then
+>   m:= CharacterTable( "M" );;
+>   torso:= [ 512372707698741056749515292734375, 405589064025344574375, 
+>   29628786742129575, 658201521662685, 215448838605, 0, 121971774375, 
+>   28098354375, 335229607, 108472455, 164587500, 4921875,,,,,, 0, 
+>   437325, 0,,,,,,, 6561, 6561, 177100, 7660, 6875, 315, 275, 0,,,, 0,,
+>   ,,,, 0, 0, 0, 3885, 525, 0,,,, 0,,,, 28, 81, 189, 9, 9, 9, 0, 540, 
+>   300, 175, 20, 15, 7,, 0, 0, 0, 0, 0, 0, 0,,,,, 0,,,,, 0, 0, 0, 0, 
+>   0, 0, 77, 45, 13, 0, 0,,,,, 0,,,,,,, 0, 0, 4, 0, 0, 9, 9, 3, 1, 0, 
+>   0, 0, 0, 0, 0, 4, 1, 1, 0,, 0, 0, 0, 0, 0,, 0, 0, 0, 0, 0, 0,, 0,, 
+>   0, 0, 0, 0, 1, 0, 0, 0, 0, 0,,,,,, 0,,, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
+>   0, 0, 0,, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
+>   0 ];;
+>   lower:= [ 512372707698741056749515292734375, 102893356234868574375, 
+>   2045161610873834, 47672538696202, 3040608610, 0, 8009187743, 
+>   783427000, 7075556, 2277590, 11945867, 18679, 52124902, 49314, 
+>   451068, 32739, 1790, 0, 7469, 0, 789, 3826, 827, 176, 212, 63, 133, 
+>   25, 3540, 131, 27, 2, 2, 0, 1032, 131, 444, 0, 38, 9, 4, 3, 3, 0, 
+>   0, 0, 19, 6, 0, 20, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 0, 4, 2, 1, 
+>   1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 
+>   0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 
+>   1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 
+>   0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 
+>   1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
+>   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ];;
+>   rat:= RationalizedMat( Irr( m ) );;
+>   constit:= rat{ [ 1, 2, 4, 5, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18,
+>   19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
+>   37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
+>   54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
+>   71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
+>   88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103,
+>   104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117,
+>   118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131,
+>   132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 
+>   146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159,
+>   160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172 ] };;
+>   cand:= PermChars( m, rec( torso:= torso, chars:= constit,
+>        lower:= lower, normalsubgroup:= [ 1 .. NrConjugacyClasses( m ) ],
+>        nonfaithful:= TrivialCharacter( m ) ) );;
+>   if Length( cand ) <> 1 then
+>     Error( "PermChars test failed" );
+>   fi;
+> fi;
+
+##
+gap> STOP_TEST( "ctblpope.tst", 1 );
+
+#############################################################################
+##
+#E
+