diff --git a/src/mmg2d/locate_2d.c b/src/mmg2d/locate_2d.c
index 0a734b1e2..5dda9a3de 100644
--- a/src/mmg2d/locate_2d.c
+++ b/src/mmg2d/locate_2d.c
@@ -167,21 +167,21 @@ int MMG2D_cutEdgeTriangle(MMG5_pMesh mesh,MMG5_int k,MMG5_int ia,MMG5_int ib) {
   prod3 = area3*area1;
 
   /* Both edges p2p3 and p1p3 corresponding to prod2 and prod3 are cut by edge ia,ib */
-  if ( prod1 > 0 && ((prod2 < 0 || prod3 < 0))) {
+  if ( prod1 > MMG2D_EPSD && ((prod2 < -MMG2D_EPSD || prod3 < -MMG2D_EPSD ))) {
     if ( (iare = MMG2D_cutEdge(mesh,pt,ppa,ppb)) ) {
       return iare;
     }
   }
 
   /* Both edges corresponding to prod1 and prod3 are cut by edge ia,ib */
-  if ( prod2 > 0 && ((prod1 < 0 || prod3 < 0))) {
+  if ( prod2 > MMG2D_EPSD && ((prod1 < -MMG2D_EPSD || prod3 < -MMG2D_EPSD ))) {
     if ( (iare = MMG2D_cutEdge(mesh,pt,ppa,ppb)) ) {
       return iare;
     }
   }
 
   /* Both edges corresponding to prod1 and prod2 are cut by edge ia,ib */
-  if ( prod3 > 0 && ((prod2 < 0 || prod1 < 0))) {
+  if ( prod3 > MMG2D_EPSD && ((prod2 < -MMG2D_EPSD || prod1 < -MMG2D_EPSD ))) {
     if ( (iare = MMG2D_cutEdge(mesh,pt,ppa,ppb)) ) {
       return iare;
     }
@@ -191,7 +191,7 @@ int MMG2D_cutEdgeTriangle(MMG5_pMesh mesh,MMG5_int k,MMG5_int ia,MMG5_int ib) {
   for(i=0; i<3; i++){
     if ( pt->v[i] == ia || ibreak ) {
       /* One vertex is ia, and the opposite edge is frankly crossed */
-      if ( (prod1 < 0) || (prod2 < 0) || (prod3 < 0) ) {
+      if ( (prod1 < -MMG2D_EPSD) || (prod2 < -MMG2D_EPSD) || (prod3 < -MMG2D_EPSD) ) {
         if ( (iare = MMG2D_cutEdge(mesh,pt,ppa,ppb)) ) {
           return iare;
         }
diff --git a/src/mmg2d/swapar_2d.c b/src/mmg2d/swapar_2d.c
index 1522d63b6..f10d2d0fe 100644
--- a/src/mmg2d/swapar_2d.c
+++ b/src/mmg2d/swapar_2d.c
@@ -78,6 +78,11 @@ int MMG2D_swapdelone(MMG5_pMesh mesh,MMG5_pSol sol,MMG5_int k,int8_t i,double cr
   arean2 = MMG2D_quickarea(mesh->point[pt0->v[0]].c,mesh->point[pt0->v[1]].c,mesh->point[pt0->v[2]].c);
   if ( cal2 > crit )  return 0;
 
+  /* Avoid creation of a flat triangle*/
+  if (fabs(arean1) < MMG2D_EPSD || fabs(arean2) < MMG2D_EPSD) {
+    return 0;
+  }
+
   if ( arean1 < 0.0 || arean2 < 0.0 || fabs((area1+area2)-(arean1+arean2)) > MMG2D_EPSD ) {
     if(mesh->info.ddebug) printf("  ## Warning: non convex configuration\n");
     return 0;