diff --git a/src/aig/gia/giaLf.c b/src/aig/gia/giaLf.c
index 130660050..3732794ee 100644
--- a/src/aig/gia/giaLf.c
+++ b/src/aig/gia/giaLf.c
@@ -1838,6 +1838,12 @@ static inline int Lf_ManDerivePart( Lf_Man_t * p, Gia_Man_t * pNew, Vec_Int_t *
     }
     pTruth = Lf_CutTruth( p, pCut );
     iLit = Kit_TruthToGia( pNew, (unsigned *)pTruth, Vec_IntSize(vLeaves), vCover, vLeaves, 0 );
+    // do not create LUT in the simple case
+    if ( Abc_Lit2Var(iLit) == 0 )
+        return iLit;
+    Vec_IntForEachEntry( vLeaves, iTemp, k )
+        if ( Abc_Lit2Var(iLit) == Abc_Lit2Var(iTemp) )
+            return iLit;
     // create mapping
     Vec_IntSetEntry( vMapping, Abc_Lit2Var(iLit), Vec_IntSize(vMapping2) );
     Vec_IntPush( vMapping2, Vec_IntSize(vLeaves) );