diff --git a/hgeometry/src/HGeometry/Plane/LowerEnvelope/Connected/BruteForce.hs b/hgeometry/src/HGeometry/Plane/LowerEnvelope/Connected/BruteForce.hs
index edbe8f310..43a3df830 100644
--- a/hgeometry/src/HGeometry/Plane/LowerEnvelope/Connected/BruteForce.hs
+++ b/hgeometry/src/HGeometry/Plane/LowerEnvelope/Connected/BruteForce.hs
@@ -26,6 +26,8 @@ import           HGeometry.Plane.LowerEnvelope.Connected.Regions
 import           HGeometry.Plane.LowerEnvelope.Connected.Type
 import           HGeometry.Point
 
+import qualified Data.Foldable as F
+import Debug.Trace
 --------------------------------------------------------------------------------
 -- * The naive O(n^4) time algorithm.
 
@@ -50,9 +52,14 @@ computeVertexForm        :: ( Plane_ plane r, Ord plane, Ord r, Fractional r, Fo
                             , Show plane, Show r
                             )
                          => set plane -> VertexForm r plane
-computeVertexForm planes = NEMap.unsafeFromMap
+computeVertexForm planes = f . NEMap.nonEmptyMap
                          . unionsWithKey mergeDefiners
+                         . traceShowWith ("foo",F.toList planes,)
                          . map (asVertex planes) $ uniqueTriplets planes
+  where
+    f = \case
+      Nothing -> error "BruteForce.computeVertexForm: no vertices !?"
+      Just x  -> x
 
 asVertex             :: (Plane_ plane r, Foldable f, Ord plane, Ord r, Fractional r)
                      => f plane -> Three plane -> Map (Point 3 r) (Definers plane)
diff --git a/hgeometry/src/HGeometry/Plane/LowerEnvelope/Connected/Randomized.hs b/hgeometry/src/HGeometry/Plane/LowerEnvelope/Connected/Randomized.hs
index 9c729b293..1dc72d725 100644
--- a/hgeometry/src/HGeometry/Plane/LowerEnvelope/Connected/Randomized.hs
+++ b/hgeometry/src/HGeometry/Plane/LowerEnvelope/Connected/Randomized.hs
@@ -66,13 +66,15 @@ computeVertexForm'    :: forall plane r.
 computeVertexForm' hs = NEMap.unsafeFromMap $ lowerEnvelope hs
   where
     n = length hs
-    r = sqrt . sqrt @Double . fromIntegral $ n
+    r = max 3 $ sqrt . sqrt @Double . fromIntegral $ n
 
     lowerEnvelope        :: Foldable set => set plane -> Map (Point 3 r) (Definers plane)
-    lowerEnvelope planes | traceShow (toList planes) False = undefined
-    lowerEnvelope planes = NEMap.mapMaybe hasNoConflict verticesRNet
-                           <>
-                           foldMap lowerEnvelopeIn triangulatedEnv
+    lowerEnvelope planes | traceShow ("LE",toList planes) False = undefined
+    lowerEnvelope planes
+        | null planes = mempty
+        | otherwise   = NEMap.mapMaybe hasNoConflict verticesRNet
+                        <>
+                        foldMap lowerEnvelopeIn triangulatedEnv
       where
         (rNet,remaining) = takeSample (round $ r * logBase 2 r) planes
 
@@ -86,7 +88,7 @@ computeVertexForm' hs = NEMap.unsafeFromMap $ lowerEnvelope hs
     lowerEnvelopeIn     :: (Foldable set, Monoid (set plane))
                         => Triangular r (Point 2 r :+ set plane)
                         -> Map (Point 3 r) (Definers plane)
-    lowerEnvelopeIn tri | traceShow (toList $ conflictListOf tri) False = undefined
+    lowerEnvelopeIn tri | traceShow ("LEI",toList $ conflictListOf tri) False = undefined
     lowerEnvelopeIn tri = Map.filterWithKey (inRegion tri)
                         $ lowerEnvelope (conflictListOf tri)
 
diff --git a/hgeometry/test/Plane/LowerEnvSpec.hs b/hgeometry/test/Plane/LowerEnvSpec.hs
index e68f68d7e..33259c3f5 100644
--- a/hgeometry/test/Plane/LowerEnvSpec.hs
+++ b/hgeometry/test/Plane/LowerEnvSpec.hs
@@ -63,9 +63,9 @@ spec :: Spec
 spec = describe "Lower Envelope tests" $ do
          it "manual" $
            let seed   = 0
-               planes = NonDegenerate $ NonEmpty.fromList [ Plane 0 1 2
-                                                          , Plane 3 (-2) 5
-                                                          , Plane (-1) 8 (-1)
+               planes = NonDegenerate $ NonEmpty.fromList [ Plane 1    0 2
+                                                          , Plane (-1) 0 3
+                                                          , Plane 0    1 10
                                                           ]
            in Randomized.computeVertexForm (mkStdGen seed) planes
               `shouldBe`