diff --git a/lib/fitfree.gi b/lib/fitfree.gi
index e45b74f4e9..33250698b5 100644
--- a/lib/fitfree.gi
+++ b/lib/fitfree.gi
@@ -166,15 +166,17 @@ local ffs,hom,U,rest,ker,r,p,l,i,depths;
 
   U!.cachedFFS:=[[ffs,r]];
 
-  # FittingFreeLiftSetup for U
-  r:=rec(inducedfrom:=ffs,
-         pcgs:=ipcgs,
-	 depths:=depths,
-         pcisom:=ffs.pcisom,
-         radical:=ker,
-         factorhom:=rest
-	);
-  SetFittingFreeLiftSetup(U,r);
+  # FittingFreeLiftSetup for U, if correct
+  if Size(RadicalGroup(Image(rest,U)))=1 then
+    r:=rec(inducedfrom:=ffs,
+          pcgs:=ipcgs,
+          depths:=depths,
+          pcisom:=ffs.pcisom,
+          radical:=ker,
+          factorhom:=rest
+          );
+    SetFittingFreeLiftSetup(U,r);
+  fi;
 
   return U;