diff --git a/graph/iterator.go b/graph/iterator.go
index 96f1587..ca17cb5 100644
--- a/graph/iterator.go
+++ b/graph/iterator.go
@@ -183,6 +183,9 @@ type IteratorStats struct {
 	ContainsCost int64
 	NextCost     int64
 	Size         int64
+	Next         int64
+	Contains     int64
+	ContainsNext int64
 }
 
 // Type enumerates the set of Iterator types.
@@ -250,6 +253,24 @@ func (t Type) String() string {
 	return types[t]
 }
 
+type StatsContainer struct {
+	IteratorStats
+	Kind   string
+	Uid    uint64
+	SubIts []StatsContainer
+}
+
+func DumpStats(it Iterator) StatsContainer {
+	var out StatsContainer
+	out.IteratorStats = it.Stats()
+	out.Kind = it.Type().String()
+	out.Uid = it.UID()
+	for _, sub := range it.SubIterators() {
+		out.SubIts = append(out.SubIts, DumpStats(sub))
+	}
+	return out
+}
+
 // Utility logging functions for when an iterator gets called Next upon, or Contains upon, as
 // well as what they return. Highly useful for tracing the execution path of a query.
 func ContainsLogIn(it Iterator, val Value) {
diff --git a/graph/iterator/all_iterator.go b/graph/iterator/all_iterator.go
index 80e471c..0a890cf 100644
--- a/graph/iterator/all_iterator.go
+++ b/graph/iterator/all_iterator.go
@@ -36,6 +36,7 @@ type Int64 struct {
 	max, min int64
 	at       int64
 	result   graph.Value
+	runstats graph.IteratorStats
 }
 
 // Creates a new Int64 with the given range.
@@ -89,6 +90,7 @@ func (it *Int64) DebugString(indent int) string {
 // Return the next integer, and mark it as the result.
 func (it *Int64) Next() bool {
 	graph.NextLogIn(it)
+	it.runstats.Next += 1
 	if it.at == -1 {
 		return graph.NextLogOut(it, nil, false)
 	}
@@ -130,6 +132,7 @@ func (it *Int64) Size() (int64, bool) {
 // withing the range, assuming the value is an int64.
 func (it *Int64) Contains(tsv graph.Value) bool {
 	graph.ContainsLogIn(it, tsv)
+	it.runstats.Contains += 1
 	v := tsv.(int64)
 	if it.min <= v && v <= it.max {
 		it.result = v
@@ -153,5 +156,7 @@ func (it *Int64) Stats() graph.IteratorStats {
 		ContainsCost: 1,
 		NextCost:     1,
 		Size:         s,
+		Next:         it.runstats.Next,
+		Contains:     it.runstats.Contains,
 	}
 }
diff --git a/graph/iterator/and_iterator.go b/graph/iterator/and_iterator.go
index c18cd70..a585cd9 100644
--- a/graph/iterator/and_iterator.go
+++ b/graph/iterator/and_iterator.go
@@ -32,6 +32,7 @@ type And struct {
 	primaryIt         graph.Iterator
 	checkList         []graph.Iterator
 	result            graph.Value
+	runstats          graph.IteratorStats
 }
 
 // Creates a new And iterator.
@@ -158,6 +159,7 @@ func (it *And) AddSubIterator(sub graph.Iterator) {
 // is therefore very important.
 func (it *And) Next() bool {
 	graph.NextLogIn(it)
+	it.runstats.Next += 1
 	for graph.Next(it.primaryIt) {
 		curr := it.primaryIt.Result()
 		if it.subItsContain(curr, nil) {
@@ -211,6 +213,7 @@ func (it *And) checkContainsList(val graph.Value, lastResult graph.Value) bool {
 // Check a value against the entire iterator, in order.
 func (it *And) Contains(val graph.Value) bool {
 	graph.ContainsLogIn(it, val)
+	it.runstats.Contains += 1
 	lastResult := it.result
 	if it.checkList != nil {
 		return it.checkContainsList(val, lastResult)
diff --git a/graph/iterator/and_iterator_optimize.go b/graph/iterator/and_iterator_optimize.go
index cb8030a7..f456926 100644
--- a/graph/iterator/and_iterator_optimize.go
+++ b/graph/iterator/and_iterator_optimize.go
@@ -17,6 +17,8 @@ package iterator
 import (
 	"sort"
 
+	"github.com/barakmich/glog"
+
 	"github.com/google/cayley/graph"
 )
 
@@ -68,7 +70,7 @@ func (it *And) Optimize() (graph.Iterator, bool) {
 
 	// And now, without changing any of the iterators, we reorder them. it_list is
 	// now a permutation of itself, but the contents are unchanged.
-	its = optimizeOrder(its)
+	its = it.optimizeOrder(its)
 
 	its = materializeIts(its)
 
@@ -87,6 +89,7 @@ func (it *And) Optimize() (graph.Iterator, bool) {
 	newAnd.tags.CopyFrom(it)
 
 	newAnd.optimizeContains()
+	glog.V(3).Infoln(it.UID(), "became", newAnd.UID())
 
 	// And close ourselves but not our subiterators -- some may still be alive in
 	// the new And (they were unchanged upon calling Optimize() on them, at the
@@ -133,7 +136,7 @@ func (_ *And) optimizeReplacement(its []graph.Iterator) graph.Iterator {
 
 // optimizeOrder(l) takes a list and returns a list, containing the same contents
 // but with a new ordering, however it wishes.
-func optimizeOrder(its []graph.Iterator) []graph.Iterator {
+func (it *And) optimizeOrder(its []graph.Iterator) []graph.Iterator {
 	var (
 		// bad contains iterators that can't be (efficiently) nexted, such as
 		// graph.Optional or graph.Not. Separate them out and tack them on at the end.
@@ -146,29 +149,35 @@ func optimizeOrder(its []graph.Iterator) []graph.Iterator {
 	// Total cost is defined as The Next()ed iterator's cost to Next() out
 	// all of it's contents, and to Contains() each of those against everyone
 	// else.
-	for _, it := range its {
-		if _, canNext := it.(graph.Nexter); !canNext {
-			bad = append(bad, it)
+	for _, root := range its {
+		if _, canNext := root.(graph.Nexter); !canNext {
+			bad = append(bad, root)
 			continue
 		}
-		rootStats := it.Stats()
+		rootStats := root.Stats()
 		cost := rootStats.NextCost
 		for _, f := range its {
-			if _, canNext := it.(graph.Nexter); !canNext {
+			if _, canNext := f.(graph.Nexter); !canNext {
 				continue
 			}
-			if f == it {
+			if f == root {
 				continue
 			}
 			stats := f.Stats()
-			cost += stats.ContainsCost
+			cost += stats.ContainsCost * (rootStats.Size / (stats.Size + 1))
 		}
 		cost *= rootStats.Size
+		if glog.V(3) {
+			glog.V(3).Infoln("And:", it.UID(), "Root:", root.UID(), "Total Cost:", cost, "Best:", bestCost)
+		}
 		if cost < bestCost {
-			best = it
+			best = root
 			bestCost = cost
 		}
 	}
+	if glog.V(3) {
+		glog.V(3).Infoln("And:", it.UID(), "Choosing:", best.UID(), "Best:", bestCost)
+	}
 
 	// TODO(barakmich): Optimization of order need not stop here. Picking a smart
 	// Contains() order based on probability of getting a false Contains() first is
@@ -320,7 +329,7 @@ func (it *And) Stats() graph.IteratorStats {
 	Size := primaryStats.Size
 	for _, sub := range it.internalIterators {
 		stats := sub.Stats()
-		NextCost += stats.ContainsCost
+		NextCost += stats.ContainsCost * (primaryStats.Size / (stats.Size + 1))
 		ContainsCost += stats.ContainsCost
 		if Size > stats.Size {
 			Size = stats.Size
@@ -330,6 +339,8 @@ func (it *And) Stats() graph.IteratorStats {
 		ContainsCost: ContainsCost * 2,
 		NextCost:     NextCost,
 		Size:         Size,
+		Next:         it.runstats.Next,
+		Contains:     it.runstats.Contains,
 	}
 
 }
diff --git a/graph/iterator/fixed_iterator.go b/graph/iterator/fixed_iterator.go
index a2d57b1..8ecda34 100644
--- a/graph/iterator/fixed_iterator.go
+++ b/graph/iterator/fixed_iterator.go
@@ -108,9 +108,10 @@ func (it *Fixed) DebugString(indent int) string {
 	if len(it.values) > 0 {
 		value = fmt.Sprint(it.values[0])
 	}
-	return fmt.Sprintf("%s(%s tags: %s Size: %d id0: %d)",
+	return fmt.Sprintf("%s(%s %d tags: %s Size: %d id0: %d)",
 		strings.Repeat(" ", indent),
 		it.Type(),
+		it.UID(),
 		it.tags.Fixed(),
 		len(it.values),
 		value,
diff --git a/graph/iterator/hasa_iterator.go b/graph/iterator/hasa_iterator.go
index b88f58b..b8aae90 100644
--- a/graph/iterator/hasa_iterator.go
+++ b/graph/iterator/hasa_iterator.go
@@ -54,6 +54,7 @@ type HasA struct {
 	dir       quad.Direction
 	resultIt  graph.Iterator
 	result    graph.Value
+	runstats  graph.IteratorStats
 }
 
 // Construct a new HasA iterator, given the triple subiterator, and the triple
@@ -143,6 +144,7 @@ func (it *HasA) DebugString(indent int) string {
 // and then Next() values out of that iterator and Contains() them against our subiterator.
 func (it *HasA) Contains(val graph.Value) bool {
 	graph.ContainsLogIn(it, val)
+	it.runstats.Contains += 1
 	if glog.V(4) {
 		glog.V(4).Infoln("Id is", it.ts.NameOf(val))
 	}
@@ -159,6 +161,7 @@ func (it *HasA) Contains(val graph.Value) bool {
 // another match is made.
 func (it *HasA) NextContains() bool {
 	for graph.Next(it.resultIt) {
+		it.runstats.ContainsNext += 1
 		link := it.resultIt.Result()
 		if glog.V(4) {
 			glog.V(4).Infoln("Quad is", it.ts.Quad(link))
@@ -193,6 +196,7 @@ func (it *HasA) NextPath() bool {
 // pull our direction out of it, and return that.
 func (it *HasA) Next() bool {
 	graph.NextLogIn(it)
+	it.runstats.Next += 1
 	if it.resultIt != nil {
 		it.resultIt.Close()
 	}
@@ -229,6 +233,9 @@ func (it *HasA) Stats() graph.IteratorStats {
 		NextCost:     tripleConstant + subitStats.NextCost,
 		ContainsCost: (fanoutFactor * nextConstant) * subitStats.ContainsCost,
 		Size:         faninFactor * subitStats.Size,
+		Next:         it.runstats.Next,
+		Contains:     it.runstats.Contains,
+		ContainsNext: it.runstats.ContainsNext,
 	}
 }
 
@@ -244,5 +251,5 @@ func (it *HasA) Close() {
 func (it *HasA) Type() graph.Type { return graph.HasA }
 
 func (it *HasA) Size() (int64, bool) {
-	return 0, true
+	return it.Stats().Size, false
 }
diff --git a/graph/iterator/iterator.go b/graph/iterator/iterator.go
index 67d8a80..ab36b7b 100644
--- a/graph/iterator/iterator.go
+++ b/graph/iterator/iterator.go
@@ -25,6 +25,10 @@ import (
 
 var nextIteratorID uint64
 
+func init() {
+	atomic.StoreUint64(&nextIteratorID, 1)
+}
+
 func NextUID() uint64 {
 	return atomic.AddUint64(&nextIteratorID, 1) - 1
 }
diff --git a/graph/iterator/linksto_iterator.go b/graph/iterator/linksto_iterator.go
index 517fc11..d13c765 100644
--- a/graph/iterator/linksto_iterator.go
+++ b/graph/iterator/linksto_iterator.go
@@ -48,6 +48,7 @@ type LinksTo struct {
 	dir       quad.Direction
 	nextIt    graph.Iterator
 	result    graph.Value
+	runstats  graph.IteratorStats
 }
 
 // Construct a new LinksTo iterator around a direction and a subiterator of
@@ -118,6 +119,7 @@ func (it *LinksTo) DebugString(indent int) string {
 // for the LinksTo.
 func (it *LinksTo) Contains(val graph.Value) bool {
 	graph.ContainsLogIn(it, val)
+	it.runstats.Contains += 1
 	node := it.ts.TripleDirection(val, it.dir)
 	if it.primaryIt.Contains(node) {
 		it.result = val
@@ -155,7 +157,9 @@ func (it *LinksTo) Optimize() (graph.Iterator, bool) {
 // Next()ing a LinksTo operates as described above.
 func (it *LinksTo) Next() bool {
 	graph.NextLogIn(it)
+	it.runstats.Next += 1
 	if graph.Next(it.nextIt) {
+		it.runstats.ContainsNext += 1
 		it.result = it.nextIt.Result()
 		return graph.NextLogOut(it, it.nextIt, true)
 	}
@@ -201,6 +205,9 @@ func (it *LinksTo) Stats() graph.IteratorStats {
 		NextCost:     nextConstant + subitStats.NextCost,
 		ContainsCost: checkConstant + subitStats.ContainsCost,
 		Size:         fanoutFactor * subitStats.Size,
+		Next:         it.runstats.Next,
+		Contains:     it.runstats.Contains,
+		ContainsNext: it.runstats.ContainsNext,
 	}
 }
 
diff --git a/graph/iterator/materialize_iterator.go b/graph/iterator/materialize_iterator.go
index 8528f4f..46f2d57 100644
--- a/graph/iterator/materialize_iterator.go
+++ b/graph/iterator/materialize_iterator.go
@@ -45,11 +45,13 @@ type Materialize struct {
 	tags        graph.Tagger
 	containsMap map[graph.Value]int
 	values      [][]result
+	actualSize  int64
 	index       int
 	subindex    int
 	subIt       graph.Iterator
 	hasRun      bool
 	aborted     bool
+	runstats    graph.IteratorStats
 }
 
 func NewMaterialize(sub graph.Iterator) *Materialize {
@@ -111,6 +113,7 @@ func (it *Materialize) Clone() graph.Iterator {
 		out.aborted = it.aborted
 		out.values = it.values
 		out.containsMap = it.containsMap
+		out.actualSize = it.actualSize
 	}
 	return out
 }
@@ -171,8 +174,10 @@ func (it *Materialize) Optimize() (graph.Iterator, bool) {
 // Otherwise, guess based on the size of the subiterator.
 func (it *Materialize) Size() (int64, bool) {
 	if it.hasRun && !it.aborted {
-		return int64(len(it.values)), true
+		glog.V(2).Infoln("returning size", it.actualSize)
+		return it.actualSize, true
 	}
+	glog.V(2).Infoln("bailing size", it.actualSize)
 	return it.subIt.Size()
 }
 
@@ -186,11 +191,14 @@ func (it *Materialize) Stats() graph.IteratorStats {
 		ContainsCost: overhead * subitStats.NextCost,
 		NextCost:     overhead * subitStats.NextCost,
 		Size:         size,
+		Next:         it.runstats.Next,
+		Contains:     it.runstats.Contains,
 	}
 }
 
 func (it *Materialize) Next() bool {
 	graph.NextLogIn(it)
+	it.runstats.Next += 1
 	if !it.hasRun {
 		it.materializeSet()
 	}
@@ -208,6 +216,7 @@ func (it *Materialize) Next() bool {
 
 func (it *Materialize) Contains(v graph.Value) bool {
 	graph.ContainsLogIn(it, v)
+	it.runstats.Contains += 1
 	if !it.hasRun {
 		it.materializeSet()
 	}
@@ -264,10 +273,17 @@ func (it *Materialize) materializeSet() {
 		tags := make(map[string]graph.Value)
 		it.subIt.TagResults(tags)
 		it.values[index] = append(it.values[index], result{id: id, tags: tags})
+		it.actualSize += 1
 		for it.subIt.NextPath() {
+			i++
+			if i > abortMaterializeAt {
+				it.aborted = true
+				break
+			}
 			tags := make(map[string]graph.Value)
 			it.subIt.TagResults(tags)
 			it.values[index] = append(it.values[index], result{id: id, tags: tags})
+			it.actualSize += 1
 		}
 	}
 	if it.aborted {
diff --git a/query/gremlin/finals.go b/query/gremlin/finals.go
index bdd7de2..a82da13 100644
--- a/query/gremlin/finals.go
+++ b/query/gremlin/finals.go
@@ -15,6 +15,8 @@
 package gremlin
 
 import (
+	"encoding/json"
+
 	"github.com/barakmich/glog"
 	"github.com/robertkrimen/otto"
 
@@ -278,5 +280,9 @@ func runIteratorOnSession(it graph.Iterator, ses *Session) {
 			}
 		}
 	}
+	if glog.V(2) {
+		bytes, _ := json.MarshalIndent(graph.DumpStats(it), "", "  ")
+		glog.V(2).Infoln(string(bytes))
+	}
 	it.Close()
 }