diff --git a/src/base/abci/abc.c b/src/base/abci/abc.c
index 31a202f8c..9c3e0324e 100644
--- a/src/base/abci/abc.c
+++ b/src/base/abci/abc.c
@@ -9171,12 +9171,12 @@ usage:
 int Abc_CommandLutCasDec( Abc_Frame_t * pAbc, int argc, char ** argv )
 {
     extern Abc_Ntk_t * Abc_NtkLutCascadeGen( int nLutSize, int nStages, int nRails, int nShared, int fVerbose );
-    extern Abc_Ntk_t * Abc_NtkLutCascade2( Abc_Ntk_t * pNtk, int nLutSize, int nLuts, int nRails, int nIters, int nJRatio, int nZParam, int Seed, int fVerbose, int fVeryVerbose, char * pGuide );
-    extern void        Abc_NtkLutCascadeFile( char * pFileName, int nVarNum, int nLutSize, int nLuts, int nRails, int nIters, int nJRatio, int nZParam, int Seed, int fVerbose, int fVeryVerbose, int fPrintMyu );
+    extern Abc_Ntk_t * Abc_NtkLutCascadeOne( Abc_Ntk_t * pNtk, int nLutSize, int nLuts, int nRails, int nIters, int nJRatio, int nZParam, int fXRail, int Seed, int fVerbose, int fVeryVerbose, char * pGuide );
+    extern void        Abc_NtkLutCascadeFile( char * pFileName, int nVarNum, int nLutSize, int nLuts, int nRails, int nIters, int nJRatio, int nZParam, int Seed, int fVerbose, int fVeryVerbose, int fPrintMyu, int fPrintLev, int fXRail );
     Abc_Ntk_t * pNtk = Abc_FrameReadNtk(pAbc), * pNtkRes; char * pGuide = NULL, * pFileName = NULL;
-    int c, nVarNum = -1, nLutSize = 6, nStages = 8, nRails = 1, nShared = 2, Seed = 0, nIters = 1, nJRatio = 0, nZParam = 0, fGen = 0, fPrintMyu = 0, fVerbose = 0, fVeryVerbose = 0;
+    int c, nVarNum = -1, nLutSize = 6, nStages = 8, nRails = 1, nShared = 2, Seed = 0, nIters = 1, nJRatio = 0, nZParam = 0, fGen = 0, fPrintMyu = 0, fPrintLev = 0, fXRail = 0, fVerbose = 0, fVeryVerbose = 0;
     Extra_UtilGetoptReset();
-    while ( ( c = Extra_UtilGetopt( argc, argv, "KMRSCIJZNFgmvwh" ) ) != EOF )
+    while ( ( c = Extra_UtilGetopt( argc, argv, "KMRSCIJZNFgmlxvwh" ) ) != EOF )
     {
         switch ( c )
         {
@@ -9292,6 +9292,12 @@ int Abc_CommandLutCasDec( Abc_Frame_t * pAbc, int argc, char ** argv )
         case 'm':
             fPrintMyu ^= 1;
             break;
+        case 'l':
+            fPrintLev ^= 1;
+            break;
+        case 'x':
+            fXRail ^= 1;
+            break;
         case 'v':
             fVerbose ^= 1;
             break;
@@ -9311,7 +9317,7 @@ int Abc_CommandLutCasDec( Abc_Frame_t * pAbc, int argc, char ** argv )
             Abc_Print( -1, "The number of variables should be given on the command line using switch \"-N <num>\".\n" );
             return 1;
         }
-        Abc_NtkLutCascadeFile( pFileName, nVarNum, nLutSize, nStages, nRails, nIters, nJRatio, nZParam, Seed, fVerbose, fVeryVerbose, fPrintMyu );
+        Abc_NtkLutCascadeFile( pFileName, nVarNum, nLutSize, nStages, nRails, nIters, nJRatio, nZParam, Seed, fVerbose, fVeryVerbose, fPrintMyu, fPrintLev, fXRail );
         return 0;
     }
     if ( fGen )
@@ -9348,7 +9354,7 @@ int Abc_CommandLutCasDec( Abc_Frame_t * pAbc, int argc, char ** argv )
     }
     if ( argc == globalUtilOptind + 1 )
         pGuide = argv[globalUtilOptind];
-    pNtkRes = Abc_NtkLutCascade2( pNtk, nLutSize, nStages, nRails, nIters, nJRatio, nZParam, Seed, fVerbose, fVeryVerbose, pGuide );
+    pNtkRes = Abc_NtkLutCascadeOne( pNtk, nLutSize, nStages, nRails, nIters, nJRatio, nZParam, fXRail, Seed, fVerbose, fVeryVerbose, pGuide );
     if ( pNtkRes == NULL )
     {
         Abc_Print( -1, "LUT cascade mapping failed.\n" );
@@ -9358,7 +9364,7 @@ int Abc_CommandLutCasDec( Abc_Frame_t * pAbc, int argc, char ** argv )
     return 0;
 
 usage:
-    Abc_Print( -2, "usage: lutcasdec [-KMRCSIJZN <num>] [-F <file>] [-gmvwh]\n" );
+    Abc_Print( -2, "usage: lutcasdec [-KMRCSIJZN <num>] [-F <file>] [-gmlxvwh]\n" );
     Abc_Print( -2, "\t           decomposes the primary output functions into LUT cascades\n" );
     Abc_Print( -2, "\t-K <num> : the number of LUT inputs [default = %d]\n", nLutSize );
     Abc_Print( -2, "\t-M <num> : the maximum delay (the number of stages) [default = %d]\n", nStages );
@@ -9372,6 +9378,8 @@ usage:
     Abc_Print( -2, "\t-F <file>: a text file with truth tables in hexadecimal listed one per line\n");    
     Abc_Print( -2, "\t-g       : toggle generating random cascade with these parameters [default = %s]\n", fGen? "yes": "no" );
     Abc_Print( -2, "\t-m       : toggle printing column multiplicity statistics [default = %s]\n", fPrintMyu? "yes": "no" );
+    Abc_Print( -2, "\t-l       : toggle printing level counting statistics [default = %s]\n", fPrintLev? "yes": "no" );
+    Abc_Print( -2, "\t-x       : toggle using extended cascade decomposition [default = %s]\n", fXRail? "yes": "no" );
     Abc_Print( -2, "\t-v       : toggle verbose printout [default = %s]\n", fVerbose? "yes": "no" );
     Abc_Print( -2, "\t-w       : toggle additional verbose printout [default = %s]\n", fVeryVerbose? "yes": "no" );
     Abc_Print( -2, "\t-h       : print the command usage\n");
diff --git a/src/base/abci/abcCas.c b/src/base/abci/abcCas.c
index e1a67dad6..6942c8a2b 100644
--- a/src/base/abci/abcCas.c
+++ b/src/base/abci/abcCas.c
@@ -656,22 +656,18 @@ void Abc_LutCascadeDerive( word * p, int nVars, int nBVars, int Myu, word * pRem
 }
 
 // performs decomposition of one stage
-static inline int Abc_LutCascadeDecStage( char * pGuide, int Iter, Vec_Wrd_t * vFuncs[3], Vec_Int_t * vVarIDs, int nRVars, int nRails, int nLutSize, int nJRatio, int nZParam, int fVerbose, Vec_Wrd_t * vCas, int * pMyu )
+static inline int Abc_LutCascadeDecStage( word Guide0, char * pGuide, int Iter, Vec_Wrd_t * vFuncs[3], Vec_Int_t * vVarIDs, int nRVars, int nRails, int nLutSize, int nJRatio, int nZParam, int fVerbose, Vec_Wrd_t * vCas, int * pMyu )
 {
-    extern word Abc_TtFindBVarsSVars( word * p, int nVars, int nRVars, int nRails, int nLutSize, int fVerbose, int * pMyu, int nJRatio );
-    extern word Abc_TtFindBVarsSVars2( word * p, int nVars, int nRVars, int nRails, int nLutSize, int fVerbose, int * pMyu, int nJRatio );
+    //extern word Abc_TtFindBVarsSVars( word * p, int nVars, int nRVars, int nRails, int nLutSize, int fVerbose, int * pMyu, int nJRatio );
+    //extern word Abc_TtFindBVarsSVars2( word * p, int nVars, int nRVars, int nRails, int nLutSize, int fVerbose, int * pMyu, int nJRatio );
     assert( Vec_IntSize(vVarIDs) > nLutSize );
     assert( Vec_IntSize(vVarIDs) <= 24 );
-    //word Guide = pGuide ? 0 : Abc_TtFindBVarsSVars( Vec_WrdArray(vFuncs[0]), Vec_IntSize(vVarIDs), nRVars, nRails, nLutSize, fVerbose, pMyu, nJRatio );
-    word Guide = pGuide ? 0 : Abc_TtFindBVarsSVars2( Vec_WrdArray(vFuncs[0]), Vec_IntSize(vVarIDs), nRVars, nRails, nLutSize, fVerbose, pMyu, nZParam );
-//    if ( nZParam )
-//        Guide = pGuide ? 0 : Abc_TtFindBVarsSVars2( Vec_WrdArray(vFuncs[0]), Vec_IntSize(vVarIDs), nRVars, nRails, nLutSize, fVerbose, pMyu, nZParam );
-//    else
-//        Guide = pGuide ? 0 : Abc_TtFindBVarsSVars( Vec_WrdArray(vFuncs[0]), Vec_IntSize(vVarIDs), nRVars, nRails, nLutSize, fVerbose, pMyu, nJRatio );
+    //word Guide = pGuide ? 0 : Abc_TtFindBVarsSVars2( Vec_WrdArray(vFuncs[0]), Vec_IntSize(vVarIDs), nRVars, nRails, nLutSize, fVerbose, pMyu, nZParam );
+    word Guide = pGuide ? 0 : Guide0;
     if ( !pGuide && !Guide ) {
         if ( fVerbose )
             printf( "The function is not decomposable with %d rails.\n", nRails );
-        Vec_IntClear( vVarIDs );
+        //Vec_IntClear( vVarIDs );
         return -1;
     }
     int m, Myu = pGuide ? 1 << nRails : (Guide >> 48) & 0xFF;
@@ -722,22 +718,48 @@ static inline int Abc_LutCascadeDecStage( char * pGuide, int Iter, Vec_Wrd_t * v
     Vec_IntShrink( vVarIDs, nFVars+nSVars+nEVars );
     return nEVars;
 }
-word * Abc_LutCascadeDec( char * pGuide, word * pTruth, int nVarsOrig, Vec_Int_t * vVarIDs, int nRails, int nLutSize, int nStages, int nJRatio, int nZParam, int fVerbose, int * pnStages, int * pMyu )
+word * Abc_LutCascadeDec( char * pGuide, word * pTruth, int nVarsOrig, Vec_Int_t * vVarIDs, int nRails, int nLutSize, int nStages, int nJRatio, int nZParam, int fXRail, int fVerbose, int * pnStages, int * pMyu )
 {
+    extern Vec_Wrd_t * Abc_TtFindBVarsSVars2( word * pTruth, int nVars, int nCVars, int nRails, int nLutSize, int fVerbose, int * pMyu, int nMyuIncrease );
     word * pRes = NULL; int i, nRVars = 0, nVars = Vec_IntSize(vVarIDs);
     Vec_Wrd_t * vFuncs[3] = { Vec_WrdStart(Abc_TtWordNum(nVars)), Vec_WrdAlloc(0), Vec_WrdAlloc(0) };
     Abc_TtCopy( Vec_WrdArray(vFuncs[0]), pTruth, Abc_TtWordNum(nVars), 0 );
     Vec_Wrd_t * vCas = Vec_WrdAlloc( 100 ); Vec_WrdPush( vCas, nVarsOrig );
     if ( pnStages ) *pnStages = 0;
     for ( i = 0; Vec_IntSize(vVarIDs) > nLutSize; i++ ) {
-        nRVars = Abc_LutCascadeDecStage( pGuide, i, vFuncs, vVarIDs, nRVars, nRails, nLutSize, nJRatio, nZParam, fVerbose, vCas, i ? NULL : pMyu );
+        int nRVarsOld = nRVars;
+        Vec_Wrd_t * vGuides = Abc_TtFindBVarsSVars2( Vec_WrdArray(vFuncs[0]), Vec_IntSize(vVarIDs), nRVars, nRails, nLutSize, fVerbose, pMyu, nZParam );
+        if ( vGuides ) {
+            word Guide0 = Vec_WrdEntry(vGuides, 0);
+            Vec_WrdFree( vGuides );
+            nRVars = Abc_LutCascadeDecStage( Guide0, pGuide, i, vFuncs, vVarIDs, nRVars, nRails, nLutSize, nJRatio, nZParam, fVerbose, vCas, i ? NULL : pMyu );
+        }
+        else
+            nRVars = -1;
         if ( i+2 > nStages ) {
             if ( fVerbose )
                 printf( "The length of the cascade (%d) exceeds the max allowed number of stages (%d).\n", i+2, nStages );
             nRVars = -1;
         }
-        if ( nRVars == -1 )
+        if ( nRVars == -1 && Vec_IntSize(vVarIDs) > nLutSize-1 && fXRail ) {
+            Vec_Wrd_t * vGuides = Abc_TtFindBVarsSVars2( Vec_WrdArray(vFuncs[0]), Vec_IntSize(vVarIDs), nRVarsOld, nRails+1, nLutSize-1, fVerbose, pMyu, nZParam );
+            if ( vGuides ) {
+                word Guide0 = Vec_WrdEntry(vGuides, 0);
+                Vec_WrdFree( vGuides );
+                nRVars = Abc_LutCascadeDecStage( Guide0, pGuide, i, vFuncs, vVarIDs, nRVarsOld, nRails+1, nLutSize-1, nJRatio, nZParam, fVerbose, vCas, NULL );
+            }
+            else
+                nRVars = -1;
+            if ( i+2 > nStages ) {
+                if ( fVerbose )
+                    printf( "The length of the cascade (%d) exceeds the max allowed number of stages (%d).\n", i+2, nStages );
+                nRVars = -1;
+            }
+        }
+        if ( nRVars == -1 ) {
+            Vec_IntClear( vVarIDs );
             break;
+        }
     }
     if ( nRVars != -1 && Vec_IntSize(vVarIDs) > 0 ) {
         Abc_LutCascadeGenOne( vCas, Vec_IntSize(vVarIDs), Vec_IntArray(vVarIDs), Vec_WrdEntry(vCas, 0), Vec_WrdArray(vFuncs[0]) );
@@ -842,7 +864,7 @@ Abc_Ntk_t * Abc_NtkLutCascade( Abc_Ntk_t * pNtk, int nLutSize, int nStages, int
     Gia_ManStop( pGia );
     return pNew;
 }
-Abc_Ntk_t * Abc_NtkLutCascade2( Abc_Ntk_t * pNtk, int nLutSize, int nStages, int nRails, int nIters, int nJRatio, int nZParam, int Seed, int fVerbose, int fVeryVerbose, char * pGuide )
+Abc_Ntk_t * Abc_NtkLutCascadeOne( Abc_Ntk_t * pNtk, int nLutSize, int nStages, int nRails, int nIters, int nJRatio, int nZParam, int fXRail, int Seed, int fVerbose, int fVeryVerbose, char * pGuide )
 {
     extern Gia_Man_t *  Abc_NtkStrashToGia( Abc_Ntk_t * pNtk );
     int i, nWords     = Abc_TtWordNum(Abc_NtkCiNum(pNtk));
@@ -870,7 +892,7 @@ Abc_Ntk_t * Abc_NtkLutCascade2( Abc_Ntk_t * pNtk, int nLutSize, int nStages, int
             printf( ".\n" );
         }
 
-        word * pLuts = Abc_LutCascadeDec( pGuide, pTruth1, Abc_NtkCiNum(pNtk), vVarIDs, nRails, nLutSize, nStages, Iter >= nIters ? 1 : 0, nZParam, fVeryVerbose, NULL, NULL );
+        word * pLuts = Abc_LutCascadeDec( pGuide, pTruth1, Abc_NtkCiNum(pNtk), vVarIDs, nRails, nLutSize, nStages, Iter >= nIters ? 1 : 0, nZParam, fXRail, fVeryVerbose, NULL, NULL );
         pNew = pLuts ? Abc_NtkLutCascadeFromLuts( pLuts, Abc_NtkCiNum(pNtk), pNtk, nLutSize, fVerbose ) : NULL;
         Vec_IntFree( vVarIDs );
         
@@ -1383,7 +1405,7 @@ Vec_Wrd_t * Abc_NtkLutCasReadTruths( char * pFileName, int nVarsOrig )
   SeeAlso     []
 
 ***********************************************************************/
-void Abc_NtkLutCascadeFile( char * pFileName, int nVarsOrig, int nLutSize, int nStages, int nRails, int nIters, int nJRatio, int nZParam, int Seed, int fVerbose, int fVeryVerbose, int fPrintMyu )
+void Abc_NtkLutCascadeFile( char * pFileName, int nVarsOrig, int nLutSize, int nStages, int nRails, int nIters, int nJRatio, int nZParam, int Seed, int fVerbose, int fVeryVerbose, int fPrintMyu, int fPrintLev, int fXRail )
 {
     abctime clkStart = Abc_Clock();   
     int i, Sum = 0, nStageCount = 0, MyuMin = 0, nTotalLuts = 0, nWords = Abc_TtWordNum(nVarsOrig);
@@ -1431,7 +1453,7 @@ void Abc_NtkLutCascadeFile( char * pFileName, int nVarsOrig, int nLutSize, int n
             printf( "Decomposing %d-var function into %d-rail cascade of %d-LUTs.\n", nVars, nRails, nLutSize );
         }
         
-        word * pLuts = Abc_LutCascadeDec( NULL, pTruth, nVarsOrig, vVarIDs, nRails, nLutSize, nStages, (int)(Iter >= nIters), nZParam, fVeryVerbose, &nStageCount, &MyuMin );
+        word * pLuts = Abc_LutCascadeDec( NULL, pTruth, nVarsOrig, vVarIDs, nRails, nLutSize, nStages, (int)(Iter >= nIters), nZParam, fXRail, fVeryVerbose, &nStageCount, &MyuMin );
         Vec_IntFree( vVarIDs );
         if ( MyuMin < 50 )     MyuStats[MyuMin]++, IterReal++;
         if ( pLuts == NULL ) {
@@ -1473,7 +1495,7 @@ void Abc_NtkLutCascadeFile( char * pFileName, int nVarsOrig, int nLutSize, int n
             if ( MyuStats[i] )
                 printf( "   %2d Myu   : Function count = %8d (%6.2f %%)\n", i, MyuStats[i], 100.0*MyuStats[i]/nFuncs/IterReal );
     }
-    if ( nRails > 1 ) {
+    if ( fPrintLev ) {
         printf( "Level count statistics for %d-rail LUT cascade:\n", nRails );
         for ( i = 0; i < 50; i++ )
             if ( StageStats[i] )
diff --git a/src/misc/util/utilBSet.c b/src/misc/util/utilBSet.c
index 1e731c8e1..cd109764f 100644
--- a/src/misc/util/utilBSet.c
+++ b/src/misc/util/utilBSet.c
@@ -897,7 +897,7 @@ int Abc_SharedEvalBest( Abc_BSEval_t * p, word * pTruth, int nVars, int nCVars,
     int nBSWords = Abc_Truth6WordNum( nVars - nFVars ), CVarMask = nCVars ? Abc_InfoMask(nCVars) << (nVars - nCVars - nFVars) : 0;
     int MyuCur, Myu = Abc_TtGetCMInt( pTruth, nVars, nFVars, p->vCounts, p->vTable, p->vStore, p->vUsed, pPat );
     int nRailsCur = Abc_Base2Log( Myu ); Vec_Int_t * vLevel; 
-    assert( Myu == MyuMin && nRailsCur > nRails );
+    assert( Myu == MyuMin && nRailsCur >= nRails );
     int i, k, iSet, iStart, nSharedMax = nVars - nFVars - nRails, nRailsMin = 100; 
     Vec_WecForEachLevelStartStop( p->vSets, vLevel, i, 1, nSharedMax ) {
         Vec_IntForEachEntryDouble( vLevel, iSet, iStart, k ) {
@@ -1018,7 +1018,7 @@ word Abc_BSEvalEncode( int * pPermBest, int nVars, int nLutSize, int Shared, int
             mSVars |= (word)1 << (nVars-nLutSize+v);
     return ((word)MyuMin << 48) | (mSVars << 24) | mBVars;
 }
-word Abc_TtFindBVarsSVars2( word * pTruth, int nVars, int nCVars, int nRails, int nLutSize, int fVerbose, int * pMyu, int nMyuIncrease )
+Vec_Wrd_t * Abc_TtFindBVarsSVars2( word * pTruth, int nVars, int nCVars, int nRails, int nLutSize, int fVerbose, int * pMyu, int nMyuIncrease )
 {
     Abc_BSEval_t * p = Abc_BSEvalAlloc(); 
     int nFVars = nVars-nLutSize;
@@ -1043,7 +1043,7 @@ word Abc_TtFindBVarsSVars2( word * pTruth, int nVars, int nCVars, int nRails, in
     word * pCopy = ABC_ALLOC( word, nWords );
     Abc_TtCopy( pCopy, pTruth, nWords, 0 );
 
-    word Result = 0;
+    Vec_Wrd_t * vRes = Vec_WrdAlloc( 10 );
     int i, k, Var0, Var1, Pla2Var[32], Var2Pla[32];
     for ( i = 0; i < nVars; i++ )
         Pla2Var[i] = Var2Pla[i] = i;
@@ -1071,20 +1071,29 @@ word Abc_TtFindBVarsSVars2( word * pTruth, int nVars, int nCVars, int nRails, in
             int Shared = 0, nSetSize = 0;
             if ( MyuThis > 2 ) {
                 int SharedThis = 0, nSetSizeThis = 0;
-                int nRailsMin = Abc_SharedEvalBest( p, pCopy, nVars, nCVars, nFVars, MyuThis, nRails, 0, &SharedThis, &nSetSizeThis, p->pPat );
+                int nRailsMin = 100;
+                for ( int r = 1; r <= nRails && nRailsMin > r; r++ ) {
+                    int nRailsMinNew = Abc_SharedEvalBest( p, pCopy, nVars, nCVars, nFVars, MyuThis, r, 0, &SharedThis, &nSetSizeThis, p->pPat );
+                    if ( nRailsMinNew < 100 )
+                        nRailsMin = nRailsMinNew;
+                }
                 if ( fVerbose )
                     printf( "  RailsMyu = %3d. RailsMin = %3d. Shared = %2d. SetSize = %d.", Abc_Base2Log(MyuThis), nRailsMin, SharedThis, nSetSizeThis );
                 if ( nRailsMin <= nRails ) {
-                    assert( Abc_Base2Log(MyuThis) >= nRailsMin );
                     MyuThis  = 1 << nRailsMin;
                     Shared   = SharedThis;
                     nSetSize = nSetSizeThis;
                 }
             }
-            if ( MyuBest > MyuThis || (MyuBest == MyuThis && nSetSizeBest > nSetSize) ) {                
+            if ( MyuBest > MyuThis || (MyuBest == MyuThis && nSetSizeBest >= nSetSize) ) {
+                int fSave = MyuBest == MyuThis && nSetSizeBest == nSetSize;
                 MyuBest = MyuThis;
                 nSetSizeBest = nSetSize;
-                Result = Abc_BSEvalEncode( Pla2Var, nVars, p->nBVars, Shared, MyuBest, nSetSize );
+                word Result = Abc_BSEvalEncode( Pla2Var, nVars, p->nBVars, Shared, MyuBest, nSetSize );
+                if ( fSave ) 
+                    Vec_WrdPush( vRes, Result );
+                else
+                    Vec_WrdFill( vRes, 1, Result );
                 if ( fVerbose )
                     printf( " <== best" );
             }
@@ -1117,11 +1126,14 @@ word Abc_TtFindBVarsSVars2( word * pTruth, int nVars, int nCVars, int nRails, in
     }
     if ( !Abc_TtEqual(pCopy, pTruth, nWords) )
         printf( "Internal truth table check failed.\n" ); 
+    //printf( "%d ", Count );
 
     Abc_BSEvalFree(p);
-    if ( MyuBest > (1 << nRails) )
-        return 0;        
-    return Result;
+    if ( MyuBest > (1 << nRails) ) {
+        Vec_WrdFree(vRes);
+        return NULL;
+    }
+    return vRes;
 }
 
 ////////////////////////////////////////////////////////////////////////