diff --git a/src/objcftl.c b/src/objcftl.c
index 17db851d29..3859747c9f 100644
--- a/src/objcftl.c
+++ b/src/objcftl.c
@@ -19,12 +19,28 @@
 
 #include <src/ariths.h>
 #include <src/error.h>
+#include <src/gapstate.h>
 #include <src/gvars.h>
 #include <src/integer.h>
 #include <src/modules.h>
 #include <src/plist.h>
 
 
+static ModuleStateOffset CFTLStateOffset = -1;
+
+struct CFTLModuleState {
+    Obj WORD_STACK;
+    Obj WORD_EXPONENT_STACK;
+    Obj SYLLABLE_STACK;
+    Obj EXPONENT_STACK;
+};
+
+extern inline struct CFTLModuleState *CFTLState(void)
+{
+    return (struct CFTLModuleState *)StateSlotsAtOffset(CFTLStateOffset);
+}
+
+
 #define IS_INT_ZERO( n )  ((n) == INTOBJ_INT(0))
 
 #define GET_COMMUTE( g )  INT_INTOBJ(ELM_PLIST(commute,(g))) 
@@ -87,14 +103,14 @@ Obj CollectPolycyc (
     Obj    ipow    = ADDR_OBJ(pcp)[ PC_INVERSEPOWERS ];
     Obj    exp     = ADDR_OBJ(pcp)[ PC_EXPONENTS ];
 
-    Obj    wst  = ADDR_OBJ(pcp)[ PC_WORD_STACK ];
-    Obj    west = ADDR_OBJ(pcp)[ PC_WORD_EXPONENT_STACK ];
-    Obj    sst  = ADDR_OBJ(pcp)[ PC_SYLLABLE_STACK ];
-    Obj    est  = ADDR_OBJ(pcp)[ PC_EXPONENT_STACK ];
+    Obj    wst  = CFTLState()->WORD_STACK;
+    Obj    west = CFTLState()->WORD_EXPONENT_STACK;
+    Obj    sst  = CFTLState()->SYLLABLE_STACK;
+    Obj    est  = CFTLState()->EXPONENT_STACK;
 
     Obj    conj=0, iconj=0;   /*QQ initialize to please compiler */
 
-    Int    st, bottom = INT_INTOBJ( ADDR_OBJ(pcp)[ PC_STACK_POINTER ] );
+    Int    st, bottom = 0;
 
     Int    g, syl, h, hh;
 
@@ -296,7 +312,6 @@ Obj CollectPolycyc (
       }
     }
 
-    ADDR_OBJ(pcp)[ PC_STACK_POINTER ] = INTOBJ_INT( bottom );
     return (Obj)0;
 }
 
@@ -394,6 +409,13 @@ static Int InitLibrary (
     return 0;
 }
 
+static void InitModuleState(ModuleStateOffset offset)
+{
+    CFTLState()->WORD_STACK  = NEW_PLIST( T_PLIST, 4096 );
+    CFTLState()->WORD_EXPONENT_STACK = NEW_PLIST( T_PLIST, 4096 );
+    CFTLState()->SYLLABLE_STACK = NEW_PLIST( T_PLIST, 4096 );
+    CFTLState()->EXPONENT_STACK = NEW_PLIST( T_PLIST, 4096 );
+}
 
 /****************************************************************************
 **
@@ -411,5 +433,6 @@ static StructInitInfo module = {
 
 StructInitInfo * InitInfoPcc ( void )
 {
+    CFTLStateOffset = RegisterModuleState(sizeof(struct CFTLModuleState), InitModuleState, 0);
     return &module;
 }
diff --git a/src/objcftl.h b/src/objcftl.h
index b7dd7c9ca3..e1832f2539 100644
--- a/src/objcftl.h
+++ b/src/objcftl.h
@@ -27,14 +27,35 @@
 #define PC_DEEP_THOUGHT_BOUND       13
 #define PC_ORDERS                   14
 
+// TODO: the following stack related positions are not
+// used anymore by CollectPolycyc, and will not be used
+// anymore in future releases of the polycyclic package.
+// We should phase them out for GAP 4.10.
 #define PC_WORD_STACK               15
 #define PC_STACK_SIZE               16
 #define PC_WORD_EXPONENT_STACK      17
 #define PC_SYLLABLE_STACK           18
 #define PC_EXPONENT_STACK           19
 #define PC_STACK_POINTER            20
+// TODO: end obsolete
+
 #define PC_DEFAULT_TYPE             21
 
+/* the following are defined in polycyclic:
+
+#define PC_PCP_ELEMENTS_FAMILY          22
+#define PC_PCP_ELEMENTS_TYPE            23
+
+#define PC_COMMUTATORS                  24
+#define PC_INVERSECOMMUTATORS           25
+#define PC_COMMUTATORSINVERSE           26
+#define PC_INVERSECOMMUTATORSINVERSE    27
+
+#define PC_NILPOTENT_COMMUTE            28
+#define PC_WEIGHTS                      29
+#define PC_ABELIAN_START                30
+*/
+
 /****************************************************************************
 **
 *F * * * * * * * * * * * * * initialize module * * * * * * * * * * * * * * *