diff --git a/Grid/qcd/action/fermion/GparityWilsonImpl.h b/Grid/qcd/action/fermion/GparityWilsonImpl.h
index 0b726db9..9dca403b 100644
--- a/Grid/qcd/action/fermion/GparityWilsonImpl.h
+++ b/Grid/qcd/action/fermion/GparityWilsonImpl.h
@@ -97,42 +97,30 @@ public:
     Coordinate icoor;
 
 #ifdef GRID_SIMT
-    _Spinor tmp;
-
     const int Nsimd =SiteDoubledGaugeField::Nsimd();
     int s = acceleratorSIMTlane(Nsimd);
     St.iCoorFromIindex(icoor,s);
 
     int mmu = mu % Nd;
-    if ( SE->_around_the_world && St.parameters.twists[mmu] ) {
-      
-      int permute_lane = (sl==1) 
-    	|| ((distance== 1)&&(icoor[direction]==1))
-	|| ((distance==-1)&&(icoor[direction]==0));
 
-      if ( permute_lane ) { 
-	tmp(0) = chi(1);
-	tmp(1) = chi(0);
-      } else {
-	tmp(0) = chi(0);
-	tmp(1) = chi(1);
-      }
+    auto UU0=coalescedRead(U(0)(mu));
+    auto UU1=coalescedRead(U(1)(mu));
+    
+    //Decide whether we do a G-parity flavor twist
+    //Note: this assumes (but does not check) that sl==1 || sl==2 i.e. max 2 SIMD lanes in G-parity dir
+    //It also assumes (but does not check) that abs(distance) == 1
+    int permute_lane = (sl==1) 
+    || ((distance== 1)&&(icoor[direction]==1))
+    || ((distance==-1)&&(icoor[direction]==0));
 
-      auto UU0=coalescedRead(U(0)(mu));
-      auto UU1=coalescedRead(U(1)(mu));
+    permute_lane = permute_lane && SE->_around_the_world && St.parameters.twists[mmu]; //only if we are going around the world
 
-      mult(&phi(0),&UU0,&tmp(0));
-      mult(&phi(1),&UU1,&tmp(1));
+    //Apply the links
+    int f_upper = permute_lane ? 1 : 0;
+    int f_lower = !f_upper;
 
-    } else {
-
-      auto UU0=coalescedRead(U(0)(mu));
-      auto UU1=coalescedRead(U(1)(mu));
-
-      mult(&phi(0),&UU0,&chi(0));
-      mult(&phi(1),&UU1,&chi(1));
-
-    }
+    mult(&phi(0),&UU0,&chi(f_upper));
+    mult(&phi(1),&UU1,&chi(f_lower));
 
 #else
     typedef _Spinor vobj;