client.go      |  6 +++++-
 client_test.go | 14 +++++++-------

diff --git a/client.go b/client.go
index 5f9420fd608ba82c34f375df0504cde81fe8231a..171abd71fb525f372612bf36121efd090562eaf5 100644
--- a/client.go
+++ b/client.go
@@ -276,9 +276,13 @@
 // Calculates the number of pieces to set to Readahead priority, after the
 // Now, and Next pieces.
 func readaheadPieces(readahead, pieceLength int64) (ret int) {
+	// Expand the readahead to fit any partial pieces. Subtract 1 for the
+	// "next" piece that is assigned.
 	ret = int((readahead+pieceLength-1)/pieceLength - 1)
+	// Lengthen the "readahead tail" to smooth blockiness that occurs when the
+	// piece length is much larger than the readahead.
 	if ret < 2 {
-		ret = 2
+		ret++
 	}
 	return
 }
diff --git a/client_test.go b/client_test.go
index 8c7cc344165ff85986300333e6fc49c772faae45..cfdbd7eb5ec433f0c72b6a3b6cb8c52b21f192b4 100644
--- a/client_test.go
+++ b/client_test.go
@@ -15,6 +15,7 @@
 	_ "github.com/anacrolix/envpprof"
 	"github.com/anacrolix/utp"
 	"github.com/bradfitz/iter"
+	"github.com/stretchr/testify/assert"
 	"gopkg.in/check.v1"
 
 	"github.com/anacrolix/torrent/bencode"
@@ -295,15 +296,14 @@ 		readaheadBytes, pieceLength int64
 		readaheadPieces             int
 	}{
 		{5 * 1024 * 1024, 256 * 1024, 19},
-		{5 * 1024 * 1024, 5 * 1024 * 1024, 0},
-		{5*1024*1024 - 1, 5 * 1024 * 1024, 0},
-		{5 * 1024 * 1024, 5*1024*1024 - 1, 1},
-		{0, 5 * 1024 * 1024, -1},
+		{5 * 1024 * 1024, 5 * 1024 * 1024, 1},
+		{5*1024*1024 - 1, 5 * 1024 * 1024, 1},
+		{5 * 1024 * 1024, 5*1024*1024 - 1, 2},
+		{0, 5 * 1024 * 1024, 0},
 		{5 * 1024 * 1024, 1048576, 4},
 	} {
-		if readaheadPieces(case_.readaheadBytes, case_.pieceLength) != case_.readaheadPieces {
-			t.Fatalf("case failed: %v", case_)
-		}
+		pieces := readaheadPieces(case_.readaheadBytes, case_.pieceLength)
+		assert.Equal(t, case_.readaheadPieces, pieces, "%v", case_)
 	}
 }