diff --git a/smt/applications/mfk.py b/smt/applications/mfk.py
index b6bf8538e..d42f7c173 100644
--- a/smt/applications/mfk.py
+++ b/smt/applications/mfk.py
@@ -37,7 +37,7 @@
 
 
 class NestedLHS(object):
-    def __init__(self, nlevel, xlimits, random_state=None):
+    def __init__(self, nlevel, xlimits, random_state=None, design_space=None):
         """
         Constructor where values of options can be passed in.
 
@@ -55,6 +55,7 @@ def __init__(self, nlevel, xlimits, random_state=None):
         self.nlevel = nlevel
         self.xlimits = xlimits
         self.random_state = random_state
+        self.design_space = design_space
 
     def __call__(self, nb_samples_hifi):
         """
@@ -86,13 +87,21 @@ def __call__(self, nb_samples_hifi):
 
         doe = []
         p0 = LHS(xlimits=self.xlimits, criterion="ese", random_state=self.random_state)
-        doe.append(p0(nt[0]))
+        p0nt0 = p0(nt[0])
+        if self.design_space:
+            p0nt0, _ = self.design_space.correct_get_acting(p0nt0)
+
+        doe.append(p0nt0)
 
         for i in range(1, self.nlevel):
             p = LHS(
                 xlimits=self.xlimits, criterion="ese", random_state=self.random_state
             )
-            doe.append(p(nt[i]))
+            pnti = p(nt[i])
+            if self.design_space:
+                pnti, _ = self.design_space.correct_get_acting(pnti)
+
+            doe.append(pnti)
 
         for i in range(1, self.nlevel)[::-1]:
             ind = []