diff --git a/addbatch.go b/addbatch.go
index 73c74ba..23aa96f 100644
--- a/addbatch.go
+++ b/addbatch.go
@@ -169,7 +169,7 @@ func (t *Tree) AddBatch(keys, values [][]byte) ([]int, error) {
 
 	// if nCPU is not a power of two, cut at the highest power of two under
 	// nCPU
-	nCPU := highestPowerOfTwo(runtime.NumCPU())
+	nCPU := flp2(runtime.NumCPU())
 	l := int(math.Log2(float64(nCPU)))
 	var invalids []int
 
@@ -189,18 +189,10 @@ func (t *Tree) AddBatch(keys, values [][]byte) ([]int, error) {
 		return nil, err
 	}
 	if nLeafs < minLeafsThreshold { // CASE B
-		var excedents []kv
-		invalids, excedents, err = t.caseB(nCPU, 0, kvs)
+		invalids, err = t.caseB(nCPU, 0, kvs)
 		if err != nil {
 			return nil, err
 		}
-		// add the excedents
-		for i := 0; i < len(excedents); i++ {
-			err = t.add(0, excedents[i].k, excedents[i].v)
-			if err != nil {
-				invalids = append(invalids, excedents[i].pos)
-			}
-		}
 
 		return t.finalizeAddBatch(len(keys), invalids)
 	}
@@ -283,31 +275,22 @@ func (t *Tree) finalizeAddBatch(nKeys int, invalids []int) ([]int, error) {
 }
 
 func (t *Tree) caseA(nCPU int, kvs []kv) ([]int, error) {
-	// if len(kvs) is not a power of 2, cut at the bigger power
-	// of two under len(kvs), build the tree with that, and add
-	// later the excedents
-	kvsP2, kvsNonP2 := cutPowerOfTwo(kvs)
-	invalids, err := t.buildTreeBottomUp(nCPU, kvsP2)
+	invalids, err := t.buildTreeBottomUp(nCPU, kvs)
 	if err != nil {
 		return nil, err
 	}
-	for i := 0; i < len(kvsNonP2); i++ {
-		if err = t.add(0, kvsNonP2[i].k, kvsNonP2[i].v); err != nil {
-			invalids = append(invalids, kvsNonP2[i].pos)
-		}
-	}
 	return invalids, nil
 }
 
-func (t *Tree) caseB(nCPU, l int, kvs []kv) ([]int, []kv, error) {
+func (t *Tree) caseB(nCPU, l int, kvs []kv) ([]int, error) {
 	// get already existing keys
 	aKs, aVs, err := t.getLeafs(t.root)
 	if err != nil {
-		return nil, nil, err
+		return nil, err
 	}
 	aKvs, err := t.keysValuesToKvs(aKs, aVs)
 	if err != nil {
-		return nil, nil, err
+		return nil, err
 	}
 	// add already existing key-values to the inputted key-values
 	// kvs = append(kvs, aKvs...)
@@ -316,23 +299,20 @@ func (t *Tree) caseB(nCPU, l int, kvs []kv) ([]int, []kv, error) {
 	// proceed with CASE A
 	sortKvs(kvs)
 
-	// cutPowerOfTwo, the excedent add it as normal Tree.Add
-	kvsP2, kvsNonP2 := cutPowerOfTwo(kvs)
 	var invalids2 []int
 	if nCPU > 1 {
-		invalids2, err = t.buildTreeBottomUp(nCPU, kvsP2)
+		invalids2, err = t.buildTreeBottomUp(nCPU, kvs)
 		if err != nil {
-			return nil, nil, err
+			return nil, err
 		}
 	} else {
-		invalids2, err = t.buildTreeBottomUpSingleThread(l, kvsP2)
+		invalids2, err = t.buildTreeBottomUpSingleThread(l, kvs)
 		if err != nil {
-			return nil, nil, err
+			return nil, err
 		}
 	}
 	invalids = append(invalids, invalids2...)
-	// return the excedents which will be added at the full tree at the end
-	return invalids, kvsNonP2, nil
+	return invalids, nil
 }
 
 func (t *Tree) caseC(nCPU, l int, keysAtL [][]byte, kvs []kv) ([]int, error) {
@@ -342,7 +322,6 @@ func (t *Tree) caseC(nCPU, l int, keysAtL [][]byte, kvs []kv) ([]int, error) {
 	buckets := splitInBuckets(kvs, nCPU)
 
 	// 2. use keys at level L as roots of the subtrees under each one
-	excedentsInBucket := make([][]kv, nCPU)
 	subRoots := make([][]byte, nCPU)
 	txs := make([]db.Tx, nCPU)
 	var wg sync.WaitGroup
@@ -361,12 +340,11 @@ func (t *Tree) caseC(nCPU, l int, keysAtL [][]byte, kvs []kv) ([]int, error) {
 				hashFunction: t.hashFunction, root: keysAtL[cpu]}
 
 			// 3. do CASE B (with 1 cpu) for each key at level L
-			_, bucketExcedents, err := bucketTree.caseB(1, l, buckets[cpu])
+			_, err = bucketTree.caseB(1, l, buckets[cpu]) // TODO handle invalids
 			if err != nil {
 				panic(err) // TODO WIP
 				// return nil, err
 			}
-			excedentsInBucket[cpu] = bucketExcedents
 			subRoots[cpu] = bucketTree.root
 			wg.Done()
 		}(i)
@@ -379,9 +357,6 @@ func (t *Tree) caseC(nCPU, l int, keysAtL [][]byte, kvs []kv) ([]int, error) {
 			return nil, err
 		}
 	}
-	for i := 0; i < len(excedentsInBucket); i++ {
-		excedents = append(excedents, excedentsInBucket[i]...)
-	}
 
 	// 4. go upFromKeys from the new roots of the subtrees
 	newRoot, err := t.upFromKeys(subRoots)
@@ -544,7 +519,7 @@ func (t *Tree) keysValuesToKvs(ks, vs [][]byte) ([]kv, error) {
 		keyPath := make([]byte, t.hashFunction.Len())
 		copy(keyPath[:], ks[i])
 		kvs[i].pos = i
-		kvs[i].keyPath = ks[i]
+		kvs[i].keyPath = keyPath
 		kvs[i].k = ks[i]
 		kvs[i].v = vs[i]
 	}
@@ -715,18 +690,9 @@ func (t *Tree) getKeysAtLevel(l int) ([][]byte, error) {
 	return keys, err
 }
 
-// cutPowerOfTwo returns []kv of length that is a power of 2, and a second []kv
-// with the extra elements that don't fit in a power of 2 length
-func cutPowerOfTwo(kvs []kv) ([]kv, []kv) {
-	x := len(kvs)
-	if (x & (x - 1)) != 0 {
-		p2 := highestPowerOfTwo(x)
-		return kvs[:p2], kvs[p2:]
-	}
-	return kvs, nil
-}
-
-func highestPowerOfTwo(n int) int {
+// flp2 computes the floor power of 2, the highest power of 2 under the given
+// value.
+func flp2(n int) int {
 	res := 0
 	for i := n; i >= 1; i-- {
 		if (i & (i - 1)) == 0 {
diff --git a/addbatch_test.go b/addbatch_test.go
index 7e1e3ee..d35aa7d 100644
--- a/addbatch_test.go
+++ b/addbatch_test.go
@@ -668,13 +668,14 @@ func TestAddBatchCaseE(t *testing.T) {
 	c.Check(tree2.Root(), qt.DeepEquals, tree1.Root())
 }
 
-func TestHighestPowerOfTwo(t *testing.T) {
+func TestFlp2(t *testing.T) {
 	c := qt.New(t)
-	c.Assert(highestPowerOfTwo(31), qt.Equals, 16)
-	c.Assert(highestPowerOfTwo(32), qt.Equals, 32)
-	c.Assert(highestPowerOfTwo(33), qt.Equals, 32)
-	c.Assert(highestPowerOfTwo(63), qt.Equals, 32)
-	c.Assert(highestPowerOfTwo(64), qt.Equals, 64)
+	c.Assert(flp2(31), qt.Equals, 16)
+	c.Assert(flp2(32), qt.Equals, 32)
+	c.Assert(flp2(33), qt.Equals, 32)
+	c.Assert(flp2(63), qt.Equals, 32)
+	c.Assert(flp2(64), qt.Equals, 64)
+	c.Assert(flp2(9000), qt.Equals, 8192)
 }
 
 // func printLeafs(name string, t *Tree) {
diff --git a/tree_test.go b/tree_test.go
index 9e49da5..9cf88bd 100644
--- a/tree_test.go
+++ b/tree_test.go
@@ -267,11 +267,11 @@ func TestGenProofAndVerify(t *testing.T) {
 	}
 
 	k := BigIntToBytes(big.NewInt(int64(7)))
-	_, siblings, err := tree.GenProof(k)
+	v := BigIntToBytes(big.NewInt(int64(14)))
+	proofV, siblings, err := tree.GenProof(k)
 	c.Assert(err, qt.IsNil)
+	c.Assert(proofV, qt.DeepEquals, v)
 
-	k = BigIntToBytes(big.NewInt(int64(7)))
-	v := BigIntToBytes(big.NewInt(int64(14)))
 	verif, err := CheckProof(tree.hashFunction, k, v, tree.Root(), siblings)
 	c.Assert(err, qt.IsNil)
 	c.Check(verif, qt.IsTrue)
diff --git a/vt_test.go b/vt_test.go
index 15fb27b..0ac8055 100644
--- a/vt_test.go
+++ b/vt_test.go
@@ -61,8 +61,6 @@ func TestVirtualTreeRandomKeys(t *testing.T) {
 		values[i] = []byte{0}
 	}
 
-	// check the root for different batches of leafs
-	testVirtualTree(c, 100, keys[:1], values[:1])
 	testVirtualTree(c, 100, keys, values)
 }