diff --git a/DAS/node.py b/DAS/node.py
index a7bb4b9..abc10fe 100644
--- a/DAS/node.py
+++ b/DAS/node.py
@@ -98,13 +98,13 @@ class Node:
                     self.logger.warning("Row custody (*vpn) larger than number of rows!", extra=self.format)
                     self.rowIDs = range(self.shape.nbRows)
                 else:
-                    self.rowIDs = set(random.sample(range(self.shape.nbRows), self.vpn*self.shape.custodyRows))
+                    self.rowIDs = set(random.sample(range(self.shape.nbRows), max(self.vpn*self.shape.custodyRows, self.shape.minCustodyRows)))
 
                 if (self.vpn * self.shape.custodyCols) > self.shape.nbCols:
                     self.logger.warning("Column custody (*vpn) larger than number of columns!", extra=self.format)
                     self.columnIDs = range(self.shape.nbCols)
                 else:
-                    self.columnIDs = set(random.sample(range(self.shape.nbCols), self.vpn*self.shape.custodyCols))
+                    self.columnIDs = set(random.sample(range(self.shape.nbCols), max(self.vpn*self.shape.custodyCols, self.shape.minCustodyCols)))
 
         self.rowNeighbors = collections.defaultdict(dict)
         self.columnNeighbors = collections.defaultdict(dict)
diff --git a/DAS/shape.py b/DAS/shape.py
index 02ec6a7..f559176 100644
--- a/DAS/shape.py
+++ b/DAS/shape.py
@@ -3,7 +3,7 @@
 class Shape:
     """This class represents a set of parameters for a specific simulation."""
     def __init__(self, nbCols, nbColsK, nbRows, nbRowsK, 
-    numberNodes, failureModel, failureRate, maliciousNodes, custodyRows, custodyCols, netDegree, bwUplinkProd, run, nodeTypes):
+    numberNodes, failureModel, failureRate, maliciousNodes, custodyRows, custodyCols, minCustodyRows, minCustodyCols, netDegree, bwUplinkProd, run, nodeTypes):
         """Initializes the shape with the parameters passed in argument."""
         self.run = run
         self.numberNodes = numberNodes
@@ -17,6 +17,8 @@ class Shape:
         self.netDegree = netDegree
         self.custodyRows = custodyRows
         self.custodyCols = custodyCols
+        self.minCustodyRows = minCustodyRows
+        self.minCustodyCols = minCustodyCols
         self.bwUplinkProd = bwUplinkProd
         self.nodeTypes = nodeTypes
         self.nodeClasses = [0] + [_k for _k in nodeTypes["classes"].keys()]
@@ -34,6 +36,8 @@ class Shape:
         shastr += "-fr-"+str(self.failureRate)
         shastr += "-cusr-"+str(self.custodyRows)
         shastr += "-cusc-"+str(self.custodyCols)
+        shastr += "-mcusr-"+str(self.minCustodyRows)
+        shastr += "-mcusc-"+str(self.minCustodyCols)
         shastr += "-bwupprod-"+str(self.bwUplinkProd)
         shastr += "-nd-"+str(self.netDegree)
         shastr += "-r-"+str(self.run)
diff --git a/smallConf.py b/smallConf.py
index c5c497a..df3a546 100644
--- a/smallConf.py
+++ b/smallConf.py
@@ -76,6 +76,8 @@ proposerPublishToC = "shape.netDegree"
 validatorBasedCustody = False
 custodyRows = range(2, 3, 2)
 custodyCols = range(2, 3, 2)
+minCustodyRows = range(2, 3, 2)
+minCustodyCols = range(2, 3, 2)
 
 # Set uplink bandwidth in megabits/second
 bwUplinksProd = [200]
@@ -146,11 +148,11 @@ colsK = range(32, 65, 128)
 rowsK = range(32, 65, 128)
 
 def nextShape():
-    for nbCols, nbColsK, nbRows, nbRowsK, run, fm, fr, mn, chR, chC, nn, netDegree, bwUplinkProd, nodeTypes in itertools.product(
-        cols, colsK, rows, rowsK, runs, failureModels, failureRates, maliciousNodes,  custodyRows, custodyCols, numberNodes, netDegrees, bwUplinksProd, nodeTypesGroup):
+    for nbCols, nbColsK, nbRows, nbRowsK, run, fm, fr, mn, chR, chC, minChR, minChC, nn, netDegree, bwUplinkProd, nodeTypes in itertools.product(
+        cols, colsK, rows, rowsK, runs, failureModels, failureRates, maliciousNodes,  custodyRows, custodyCols, minCustodyRows, minCustodyCols, numberNodes, netDegrees, bwUplinksProd, nodeTypesGroup):
         # Network Degree has to be an even number
         if netDegree % 2 == 0:
-            shape = Shape(nbCols, nbColsK, nbRows, nbRowsK, nn, fm, fr, mn, chR, chC, netDegree, bwUplinkProd, run, nodeTypes)
+            shape = Shape(nbCols, nbColsK, nbRows, nbRowsK, nn, fm, fr, mn, chR, chC, minChR, minChC, netDegree, bwUplinkProd, run, nodeTypes)
             yield shape
 
 def evalConf(self, param, shape = None):