diff --git a/fuzz.go b/fuzz.go
index df96b8c..59dc5e0 100644
--- a/fuzz.go
+++ b/fuzz.go
@@ -2,16 +2,41 @@
 
 package tdigest
 
+import (
+	"bytes"
+	"fmt"
+	"log"
+
+	"github.com/davecgh/go-spew/spew"
+)
+
 func Fuzz(data []byte) int {
 	v := new(TDigest)
 	err := v.UnmarshalBinary(data)
 	if err != nil {
 		return 0
 	}
-	_, err = v.MarshalBinary()
+
+	remarshaled, err := v.MarshalBinary()
 	if err != nil {
 		panic(err)
 	}
-	return 1
 
+	if !bytes.HasPrefix(data, remarshaled) {
+		panic(fmt.Sprintf("not equal: \n%v\nvs\n%v", data, remarshaled))
+	}
+
+	for q := float64(0.1); q <= 1.0; q += 0.05 {
+		prev, this := v.Quantile(q-0.1), v.Quantile(q)
+		if prev-this > 1e-100 { // Floating point math makes this slightly imprecise.
+			log.Printf("v: %s", spew.Sprint(v))
+			log.Printf("q: %v", q)
+			log.Printf("prev: %v", prev)
+			log.Printf("this: %v", this)
+			panic("quantiles should only increase")
+		}
+	}
+
+	v.Add(1, 1)
+	return 1
 }
diff --git a/fuzz_test.go b/fuzz_test.go
index 9c92f05..45ddf9b 100644
--- a/fuzz_test.go
+++ b/fuzz_test.go
@@ -1,22 +1,44 @@
 package tdigest
 
-import "testing"
+import (
+	"bytes"
+	"testing"
+
+	"github.com/davecgh/go-spew/spew"
+)
 
 func TestFuzzPanicRegressions(t *testing.T) {
 	// This test contains a list of byte sequences discovered by
 	// github.com/dvyukov/go-fuzz which, at one time, caused tdigest to panic. The
 	// test just makes sure that they no longer cause a panic.
 	testcase := func(crasher []byte) func(*testing.T) {
-		return func(*testing.T) {
+		return func(t *testing.T) {
 			v := new(TDigest)
 			err := v.UnmarshalBinary(crasher)
 			if err != nil {
 				return
 			}
-			_, err = v.MarshalBinary()
+			remarshaled, err := v.MarshalBinary()
 			if err != nil {
-				panic(err)
+				t.Fatalf("marshal error: %v", err)
+			}
+
+			if !bytes.HasPrefix(crasher, remarshaled) {
+				t.Fatalf("not equal: \n%v\nvs\n%v", crasher, remarshaled)
+			}
+
+			for q := float64(0.1); q <= 1.0; q += 0.05 {
+				prev, this := v.Quantile(q-0.1), v.Quantile(q)
+				if prev-this > 1e-100 { // Floating point math makes this slightly imprecise.
+					t.Logf("v: %s", spew.Sprint(v))
+					t.Logf("q: %v", q)
+					t.Logf("prev: %v", prev)
+					t.Logf("this: %v", this)
+					t.Fatal("quantiles should only increase")
+				}
 			}
+
+			v.Add(1, 1)
 		}
 	}
 	t.Run("fuzz1", testcase([]byte{
@@ -32,5 +54,31 @@ func TestFuzzPanicRegressions(t *testing.T) {
 		0x37, 0x35, 0x37, 0x36, 0x37, 0x37, 0x37, 0x38,
 		0x37, 0x39, 0x28,
 	}))
-
+	t.Run("fuzz3", testcase([]byte{
+		0x80, 0x0c, 0x01, 0x00, 0x00, 0x00, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x02, 0x00,
+		0x00, 0x00, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0xbf,
+	}))
+	t.Run("fuzz4", testcase([]byte{
+		0x80, 0x0c, 0x01, 0x00, 0x00, 0x00, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x02, 0x00,
+		0x00, 0x00, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x63, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x4e,
+	}))
+	t.Run("fuzz5", testcase([]byte{
+		0x80, 0x0c, 0x01, 0x00, 0x00, 0x00, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x02, 0x00,
+		0x00, 0x00, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x00, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x30, 0x00, 0x30, 0x30, 0x30, 0x30, 0x30, 0x30,
+		0x92, 0x00,
+	}))
 }
diff --git a/serde.go b/serde.go
index 3b32679..a8f3d8e 100644
--- a/serde.go
+++ b/serde.go
@@ -5,6 +5,7 @@ import (
 	"encoding/binary"
 	"fmt"
 	"io"
+	"math"
 )
 
 const (
@@ -39,11 +40,11 @@ func unmarshalBinary(d *TDigest, p []byte) error {
 	r := &binaryReader{r: bytes.NewReader(p)}
 	r.readValue(&mv)
 	if mv != magic {
-		return fmt.Errorf("invalid header magic value, data might be corrupted: %d", mv)
+		return fmt.Errorf("data corruption detected: invalid header magic value %d", mv)
 	}
 	r.readValue(&ev)
 	if ev != encodingVersion {
-		return fmt.Errorf("invalid encoding version: %d", ev)
+		return fmt.Errorf("data corruption detected: invalid encoding version %d", ev)
 	}
 	r.readValue(&d.compression)
 	r.readValue(&n)
@@ -51,7 +52,7 @@ func unmarshalBinary(d *TDigest, p []byte) error {
 		return r.err
 	}
 	if n < 0 {
-		return fmt.Errorf("invalid n, cannot be negative: %v", n)
+		return fmt.Errorf("data corruption detected: number of centroids cannot be negative, have %v", n)
 	}
 	if n > 1<<20 {
 		return fmt.Errorf("invalid n, cannot be greater than 2^20: %v", n)
@@ -64,7 +65,19 @@ func unmarshalBinary(d *TDigest, p []byte) error {
 		if r.err != nil {
 			return r.err
 		}
+		if c.count < 0 {
+			return fmt.Errorf("data corruption detected: negative count: %d", c.count)
+		}
+		if i > 0 {
+			prev := d.centroids[i-1]
+			if c.mean < prev.mean {
+				return fmt.Errorf("data corruption detected: centroid %d has lower mean (%v) than preceding centroid %d (%v)", i, c.mean, i-1, prev.mean)
+			}
+		}
 		d.centroids[i] = c
+		if c.count > math.MaxInt64-d.countTotal {
+			return fmt.Errorf("data corruption detected: centroid total size overflow")
+		}
 		d.countTotal += c.count
 	}