diff --git a/zstd_stream_skippable_test.go b/zstd_stream_skippable_test.go
new file mode 100644
index 0000000..5d6472b
--- /dev/null
+++ b/zstd_stream_skippable_test.go
@@ -0,0 +1,70 @@
+package zstd
+
+import (
+	"bytes"
+	"encoding/binary"
+	"io"
+	"io/ioutil"
+	"testing"
+)
+
+// skippableFrame returns a valid zstd skippable frame carrying 4 bytes of user data.
+// https://github.com/facebook/zstd/blob/dev/doc/zstd_compression_format.md#skippable-frames
+func skippableFrame(userValue uint32) []byte {
+	skipFrame := make([]byte, 12)
+	binary.LittleEndian.PutUint32(skipFrame, 0x184D2A50) // user-defined skippable magic
+	binary.LittleEndian.PutUint32(skipFrame[4:], 4)      // frame content size
+	binary.LittleEndian.PutUint32(skipFrame[8:], userValue)
+	return skipFrame
+}
+
+// TestDecompressTrailingSkippableFrame verifies that one-shot Decompress accepts a
+// valid zstd stream followed by a trailing skippable frame. The payload is highly
+// compressible, so the compressed input is tiny relative to its decompressed size;
+// that is the shape where the streaming fallback previously stopped after the first
+// frame and reported unexpected EOF on the trailing skippable frame.
+// Regression context: https://github.com/DataDog/zstd/issues/129
+func TestDecompressTrailingSkippableFrame(t *testing.T) {
+	totalSize := 1_000_001
+	rawData := make([]byte, totalSize) // all zeros: highly compressible
+
+	compressed, err := Compress(nil, rawData)
+	if err != nil {
+		t.Fatal(err)
+	}
+	compressed = append(compressed, skippableFrame(12345)...)
+
+	decompressed, err := Decompress(nil, compressed)
+	if err != nil {
+		t.Fatalf("Decompress: %s", err)
+	}
+	if !bytes.Equal(rawData, decompressed) {
+		t.Fatal("decompressed data does not match original")
+	}
+}
+
+// TestReaderTrailingSkippableFrame verifies the same through the streaming reader.
+func TestReaderTrailingSkippableFrame(t *testing.T) {
+	totalSize := 1_000_001
+	rawData := make([]byte, totalSize)
+	r := NewRandBytes()
+	if _, err := io.ReadFull(r, rawData); err != nil && err != io.EOF {
+		t.Fatal(err)
+	}
+
+	compressed, err := Compress(nil, rawData)
+	if err != nil {
+		t.Fatal(err)
+	}
+	compressed = append(compressed, skippableFrame(12345)...)
+
+	reader := NewReader(bytes.NewReader(compressed))
+	defer reader.Close()
+	decompressed, err := ioutil.ReadAll(reader)
+	if err != nil {
+		t.Fatalf("stream reader: %s", err)
+	}
+	if !bytes.Equal(rawData, decompressed) {
+		t.Fatal("decompressed data does not match original")
+	}
+}