diff --git a/doc.go b/doc.go
new file mode 100644
index 0000000..deb2de9
--- /dev/null
+++ b/doc.go
@@ -0,0 +1,22 @@
+// Copyright 2019, LightStep Inc.
+
+/*
+Package varopt is an implementation of VarOpt, an unbiased weighted
+sampling algorithm described in the paper "Stream sampling for
+variance-optimal estimation of subset sums"
+https://arxiv.org/pdf/0803.0473.pdf (2008), by Edith Cohen, Nick
+Duffield, Haim Kaplan, Carsten Lund, and Mikkel Thorup.
+
+VarOpt is a reservoir-type sampler that maintains a fixed-size sample
+and provides a mechanism for merging unequal-weight samples.
+
+This package also includes a simple reservoir sampling algorithm,
+often useful in conjunction with weighed reservoir sampling, using
+Algorithm R from "Random sampling with a
+reservoir", https://en.wikipedia.org/wiki/Reservoir_sampling#Algorithm_R
+(1985), by Jeffrey Vitter.
+
+See https://github.com/lightstep/varopt/blob/master/README.md for
+more detail.
+*/
+package varopt
diff --git a/frequency_test.go b/frequency_test.go
index 9da7bca..e4b3429 100644
--- a/frequency_test.go
+++ b/frequency_test.go
@@ -35,7 +35,7 @@ var colors = []curve{
 // While the number of expected points per second is uniform, the
 // output sample weights are expected to match the original
 // frequencies.
-func ExampleFrequency() {
+func ExampleVaropt_GetOriginalWeight() {
 	// Number of points.
 	const totalCount = 1e6
 
diff --git a/simple.go b/simple.go
index 7d0fb7f..6ff64f1 100644
--- a/simple.go
+++ b/simple.go
@@ -13,14 +13,20 @@ type Simple struct {
 	capacity int
 	observed int
 	buffer   []Sample
+	rnd      *rand.Rand
 }
 
-func NewSimple(capacity int) *Simple {
+// NewSimple returns a simple reservoir sampler with given capacity
+// (i.e., reservoir size) and random number generator.
+func NewSimple(capacity int, rnd *rand.Rand) *Simple {
 	return &Simple{
 		capacity: capacity,
+		rnd:      rnd,
 	}
 }
 
+// Add considers a new observation for the sample.  Items have unit
+// weight.
 func (s *Simple) Add(span Sample) {
 	s.observed++
 
@@ -34,28 +40,29 @@ func (s *Simple) Add(span Sample) {
 	}
 
 	// Give this a capacity/observed chance of replacing an existing entry.
-	index := rand.Intn(s.observed)
+	index := s.rnd.Intn(s.observed)
 	if index < s.capacity {
 		s.buffer[index] = span
 	}
 }
 
+// Get returns the i'th selected item from the sample.
 func (s *Simple) Get(i int) Sample {
 	return s.buffer[i]
 }
 
+// Get returns the number of items in the sample.  If the reservoir is
+// full, Size() equals Capacity().
 func (s *Simple) Size() int {
 	return len(s.buffer)
 }
 
+// Weight returns the adjusted weight of each item in the sample.
 func (s *Simple) Weight() float64 {
 	return float64(s.observed) / float64(s.Size())
 }
 
-func (s *Simple) Prob() float64 {
-	return 1 / s.Weight()
-}
-
-func (s *Simple) Observed() int {
+// Count returns the number of items that were observed.
+func (s *Simple) Count() int {
 	return s.observed
 }
diff --git a/simple_test.go b/simple_test.go
index 8c83500..c70503e 100644
--- a/simple_test.go
+++ b/simple_test.go
@@ -3,6 +3,7 @@
 package varopt_test
 
 import (
+	"math/rand"
 	"testing"
 
 	"github.com/lightstep/varopt"
@@ -19,7 +20,9 @@ func TestSimple(t *testing.T) {
 		epsilon        = 0.01
 	)
 
-	ss := varopt.NewSimple(sampleSize)
+	rnd := rand.New(rand.NewSource(17167))
+
+	ss := varopt.NewSimple(sampleSize, rnd)
 
 	psum := 0.
 	for i := 0; i < popSize; i++ {
diff --git a/varopt.go b/varopt.go
index 4dd8ea3..1856614 100644
--- a/varopt.go
+++ b/varopt.go
@@ -36,6 +36,9 @@ type Varopt struct {
 	totalWeight float64
 }
 
+// Sample is an empty interface that represents a sample item.
+// Sampling algorithms treat these as opaque, as their weight is
+// passed in separately.
 type Sample interface{}
 
 type vsample struct {
@@ -45,6 +48,8 @@ type vsample struct {
 
 type largeHeap []vsample
 
+// New returns a new Varopt sampler with given capacity (i.e.,
+// reservoir size) and random number generator.
 func New(capacity int, rnd *rand.Rand) *Varopt {
 	return &Varopt{
 		capacity: capacity,
@@ -52,6 +57,7 @@ func New(capacity int, rnd *rand.Rand) *Varopt {
 	}
 }
 
+// Add considers a new observation for the sample with given weight.
 func (s *Varopt) Add(sample Sample, weight float64) {
 	individual := vsample{
 		sample: sample,
@@ -131,6 +137,9 @@ func (s *Varopt) Get(i int) (Sample, float64) {
 	return s.T[i-len(s.L)].sample, s.tau
 }
 
+// GetOriginalWeight returns the original input weight of the sample
+// item that was passed to Add().  This can be useful for computing a
+// frequency from the adjusted sample weight.
 func (s *Varopt) GetOriginalWeight(i int) float64 {
 	if i < len(s.L) {
 		return s.L[i].weight
@@ -139,22 +148,31 @@ func (s *Varopt) GetOriginalWeight(i int) float64 {
 	return s.T[i-len(s.L)].weight
 }
 
+// Capacity returns the size of the reservoir.  This is the maximum
+// size of the sample.
 func (s *Varopt) Capacity() int {
 	return s.capacity
 }
 
+// Size returns the current number of items in the sample.  If the
+// reservoir is full, this returns Capacity().
 func (s *Varopt) Size() int {
 	return len(s.L) + len(s.T)
 }
 
+// TotalWeight returns the sum of weights that were passed to Add().
 func (s *Varopt) TotalWeight() float64 {
 	return s.totalWeight
 }
 
+// TotalCount returns the number of calls to Add().
 func (s *Varopt) TotalCount() int {
 	return s.totalCount
 }
 
+// Tau returns the current large-weight threshold.  Weights larger
+// than Tau() carry their exact weight int he sample.  See the VarOpt
+// paper for details.
 func (s *Varopt) Tau() float64 {
 	return s.tau
 }
diff --git a/varopt_test.go b/varopt_test.go
index 16786ab..3d6eec3 100644
--- a/varopt_test.go
+++ b/varopt_test.go
@@ -23,9 +23,7 @@ const (
 	sampleProb     = 0.001
 	sampleSize int = popSize * sampleProb
 
-	// TODO epsilon is somewhat variable b/c we're using the
-	// static rand w/o a fixed seed for the test.
-	epsilon = 0.06
+	epsilon = 0.08
 )
 
 func TestUnbiased(t *testing.T) {
@@ -108,7 +106,7 @@ func testUnbiased(t *testing.T, bbr, bsr float64) {
 
 			for _, blockList := range blockLists {
 				for _, block := range blockList {
-					simple := varopt.NewSimple(sampleSize)
+					simple := varopt.NewSimple(sampleSize, rnd)
 
 					for _, s := range block {
 						simple.Add(s)
diff --git a/weighted_test.go b/weighted_test.go
index e545fbd..1e82043 100644
--- a/weighted_test.go
+++ b/weighted_test.go
@@ -16,7 +16,7 @@ type packet struct {
 	protocol string
 }
 
-func ExampleWeighted() {
+func ExampleNew() {
 	const totalPackets = 1e6
 	const sampleRatio = 0.01