diff --git a/zstd/fuzz_test.go b/zstd/fuzz_test.go
new file mode 100644
index 0000000000..2b30f6af15
--- /dev/null
+++ b/zstd/fuzz_test.go
@@ -0,0 +1,186 @@
+// +build gofuzzbeta
+
+package zstd_test
+
+import (
+	"archive/tar"
+	"bytes"
+	"fmt"
+	"io"
+	"io/ioutil"
+	"os"
+	"runtime"
+	"testing"
+
+	"github.com/klauspost/compress/zstd"
+)
+
+func FuzzCompress(f *testing.F) {
+	var dec *zstd.Decoder
+	var encs [zstd.SpeedBestCompression + 1]*zstd.Encoder
+	var encsD [zstd.SpeedBestCompression + 1]*zstd.Encoder
+
+	runtime.GOMAXPROCS(2)
+	// Also tests with dictionaries...
+	const testDicts = false
+
+	initEnc := func() func() {
+		dict, err := ioutil.ReadFile("testdata/d0.dict")
+		if err != nil {
+			panic(err)
+		}
+		dec, err = zstd.NewReader(nil, zstd.WithDecoderConcurrency(1), zstd.WithDecoderDicts(dict))
+		if err != nil {
+			panic(err)
+		}
+		for level := zstd.SpeedFastest; level <= zstd.SpeedBestCompression; level++ {
+			encs[level], err = zstd.NewWriter(nil, zstd.WithEncoderCRC(true), zstd.WithEncoderLevel(level), zstd.WithEncoderConcurrency(2), zstd.WithWindowSize(128<<10), zstd.WithZeroFrames(true), zstd.WithLowerEncoderMem(true))
+			if testDicts {
+				encsD[level], err = zstd.NewWriter(nil, zstd.WithEncoderCRC(true), zstd.WithEncoderLevel(level), zstd.WithEncoderConcurrency(2), zstd.WithWindowSize(128<<10), zstd.WithZeroFrames(true), zstd.WithEncoderDict(dict), zstd.WithLowerEncoderMem(true), zstd.WithLowerEncoderMem(true))
+			}
+		}
+		return func() {
+			dec.Close()
+			for _, enc := range encs {
+				if enc != nil {
+					enc.Close()
+				}
+			}
+			if testDicts {
+				for _, enc := range encsD {
+					if enc != nil {
+						enc.Close()
+					}
+				}
+			}
+		}
+	}
+
+	f.Cleanup(initEnc())
+	// Run test against out decoder
+	var dst bytes.Buffer
+
+	// Create a buffer that will usually be too small.
+	corpus, err := os.Open("testdata/corpus.tar.zst")
+	if err != nil {
+		f.Fatal(err)
+	}
+	err = dec.Reset(corpus)
+	if err != nil {
+		f.Fatal(err)
+	}
+	tr := tar.NewReader(dec)
+load_corpus:
+	for {
+		header, err := tr.Next()
+		switch err {
+		case io.EOF:
+			break load_corpus
+		default:
+			f.Fatal(err)
+		case nil:
+		}
+		if header.Typeflag != tar.TypeReg {
+			continue
+		}
+		tmp := make([]byte, header.Size)
+		_, err = io.ReadFull(tr, tmp)
+		if err != nil {
+			f.Fatal(err)
+		}
+		if header.Size > 100<<10 {
+			continue
+		}
+		f.Add(tmp)
+	}
+	corpus.Close()
+	dec.Reset(nil)
+
+	f.Fuzz(func(t *testing.T, data []byte) {
+		if len(data) > 1<<20 {
+			return
+		}
+		var bufSize = len(data)
+		if bufSize > 2 {
+			// Make deterministic size
+			bufSize = int(data[0]) | int(data[1])<<8
+			if bufSize >= len(data) {
+				bufSize = len(data) / 2
+			}
+		}
+
+		for level := zstd.SpeedFastest; level <= zstd.SpeedBestCompression; level++ {
+			enc := encs[level]
+			dst.Reset()
+			enc.Reset(&dst)
+			n, err := enc.Write(data)
+			if err != nil {
+				t.Fatal(err)
+			}
+			if n != len(data) {
+				t.Fatal(fmt.Sprintln("Level", level, "Short write, got:", n, "want:", len(data)))
+			}
+
+			encoded := enc.EncodeAll(data, make([]byte, 0, bufSize))
+			got, err := dec.DecodeAll(encoded, make([]byte, 0, bufSize))
+			if err != nil {
+				t.Fatal(fmt.Sprintln("Level", level, "DecodeAll error:", err, "\norg:", len(data), "\nencoded", len(encoded)))
+			}
+			if !bytes.Equal(got, data) {
+				t.Fatal(fmt.Sprintln("Level", level, "DecodeAll output mismatch\n", len(got), "org: \n", len(data), "(want)", "\nencoded:", len(encoded)))
+			}
+
+			err = enc.Close()
+			if err != nil {
+				t.Fatal(fmt.Sprintln("Level", level, "Close (buffer) error:", err))
+			}
+			encoded2 := dst.Bytes()
+			if !bytes.Equal(encoded, encoded2) {
+				got, err = dec.DecodeAll(encoded2, got[:0])
+				if err != nil {
+					t.Fatal(fmt.Sprintln("Level", level, "DecodeAll (buffer) error:", err, "\norg:", len(data), "\nencoded", len(encoded2)))
+				}
+				if !bytes.Equal(got, data) {
+					t.Fatal(fmt.Sprintln("Level", level, "DecodeAll (buffer) output mismatch\n", len(got), "org: \n", len(data), "(want)", "\nencoded:", len(encoded2)))
+				}
+			}
+			if !testDicts {
+				continue
+			}
+			enc = encsD[level]
+			dst.Reset()
+			enc.Reset(&dst)
+			n, err = enc.Write(data)
+			if err != nil {
+				t.Fatal(err)
+			}
+			if n != len(data) {
+				t.Fatal(fmt.Sprintln("Dict Level", level, "Short write, got:", n, "want:", len(data)))
+			}
+
+			encoded = enc.EncodeAll(data, encoded[:0])
+			got, err = dec.DecodeAll(encoded, got[:0])
+			if err != nil {
+				t.Fatal(fmt.Sprintln("Dict Level", level, "DecodeAll error:", err, "\norg:", len(data), "\nencoded", len(encoded)))
+			}
+			if !bytes.Equal(got, data) {
+				t.Fatal(fmt.Sprintln("Dict Level", level, "DecodeAll output mismatch\n", len(got), "org: \n", len(data), "(want)", "\nencoded:", len(encoded)))
+			}
+
+			err = enc.Close()
+			if err != nil {
+				t.Fatal(fmt.Sprintln("Dict Level", level, "Close (buffer) error:", err))
+			}
+			encoded2 = dst.Bytes()
+			if !bytes.Equal(encoded, encoded2) {
+				got, err = dec.DecodeAll(encoded2, got[:0])
+				if err != nil {
+					t.Fatal(fmt.Sprintln("Dict Level", level, "DecodeAll (buffer) error:", err, "\norg:", len(data), "\nencoded", len(encoded2)))
+				}
+				if !bytes.Equal(got, data) {
+					t.Fatal(fmt.Sprintln("Dict Level", level, "DecodeAll (buffer) output mismatch\n", len(got), "org: \n", len(data), "(want)", "\nencoded:", len(encoded2)))
+				}
+			}
+		}
+	})
+}
diff --git a/zstd/testdata/corpus.tar.zst b/zstd/testdata/corpus.tar.zst
new file mode 100644
index 0000000000..6dcf1ebe3d
Binary files /dev/null and b/zstd/testdata/corpus.tar.zst differ
diff --git a/zstd/zstd_test.go b/zstd/zstd_test.go
index baa51c3da1..76d2ca925c 100644
--- a/zstd/zstd_test.go
+++ b/zstd/zstd_test.go
@@ -11,12 +11,12 @@ import (
 
 func TestMain(m *testing.M) {
 	ec := m.Run()
-	if ec == 0 && runtime.NumGoroutine() > 1 {
+	if ec == 0 && runtime.NumGoroutine() > 2 {
 		n := 0
 		for n < 60 {
 			n++
 			time.Sleep(time.Second)
-			if runtime.NumGoroutine() == 1 {
+			if runtime.NumGoroutine() == 2 {
 				os.Exit(0)
 			}
 		}