diff --git a/key_test.go b/key_test.go
index 82129dac..2038a2e6 100644
--- a/key_test.go
+++ b/key_test.go
@@ -190,9 +190,6 @@ func TestGenerateEd25519(t *testing.T) {
 	if _, err = key.MarshalPKIXPublicKeyPEM(); err != nil {
 		t.Fatal(err)
 	}
-	if _, err = key.MarshalPKCS1PrivateKeyPEM(); err != nil {
-		t.Fatal(err)
-	}
 }
 
 func TestSign(t *testing.T) {
@@ -431,9 +428,7 @@ func TestMarshalEd25519(t *testing.T) {
 		t.Fatal("invalid cert pem bytes")
 	}
 
-	if _, err = key.MarshalPKCS1PrivateKeyPEM(); err != nil {
-		t.Fatal(err)
-	}
+	// NOTE: Ed25519 cannot be marshalled to PEM.
 
 	if _, err := key.MarshalPKCS1PrivateKeyDER(); err != nil {
 		t.Fatal(err)
diff --git a/ssl_test.go b/ssl_test.go
index db48aeb2..b1309c59 100644
--- a/ssl_test.go
+++ b/ssl_test.go
@@ -193,7 +193,7 @@ func SimpleConnTest(t testing.TB, constructor func(
 		}
 
 		buf := bytes.NewBuffer(make([]byte, 0, len(data)))
-		_, err = io.CopyN(buf, server, int64(len(data)))
+		_, err = io.Copy(buf, server)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -201,10 +201,8 @@ func SimpleConnTest(t testing.TB, constructor func(
 			t.Fatal("mismatched data")
 		}
 
-		err = server.Close()
-		if err != nil {
-			t.Fatal(err)
-		}
+		// Only one side gets a clean close because closing needs to write a terminator.
+		_ = server.Close()
 	}()
 	wg.Wait()
 }
@@ -223,10 +221,10 @@ func close_both(closer1, closer2 io.Closer) {
 	wg.Wait()
 }
 
-func ClosingTest(t testing.TB, constructor func(
+func ClosingTest(t *testing.T, constructor func(
 	t testing.TB, conn1, conn2 net.Conn) (sslconn1, sslconn2 HandshakingConn)) {
 
-	run_test := func(close_tcp bool, server_writes bool) {
+	run_test := func(t *testing.T, close_tcp bool, server_writes bool) {
 		server_conn, client_conn := NetPipe(t)
 		defer server_conn.Close()
 		defer client_conn.Close()
@@ -246,12 +244,34 @@ func ClosingTest(t testing.TB, constructor func(
 		}
 
 		var wg sync.WaitGroup
+
+		// If we're killing the TCP connection, make sure we handshake first
+		if close_tcp {
+			wg.Add(2)
+			go func() {
+				defer wg.Done()
+				err := sslconn1.Handshake()
+				if err != nil {
+					t.Error(err)
+				}
+			}()
+			go func() {
+				defer wg.Done()
+				err := sslconn2.Handshake()
+				if err != nil {
+					t.Error(err)
+				}
+			}()
+			wg.Wait()
+		}
+
 		wg.Add(2)
 		go func() {
 			defer wg.Done()
 			_, err := sslconn1.Write([]byte("hello"))
 			if err != nil {
-				t.Fatal(err)
+				t.Error(err)
+				return
 			}
 			if close_tcp {
 				err = conn1.Close()
@@ -259,28 +279,37 @@ func ClosingTest(t testing.TB, constructor func(
 				err = sslconn1.Close()
 			}
 			if err != nil {
-				t.Fatal(err)
+				t.Error(err)
 			}
 		}()
 
 		go func() {
 			defer wg.Done()
 			data, err := ioutil.ReadAll(sslconn2)
-			if err != nil {
-				t.Fatal(err)
-			}
 			if !bytes.Equal(data, []byte("hello")) {
-				t.Fatal("bytes don't match")
+				t.Error("bytes don't match")
+			}
+			if !close_tcp && err != nil {
+				t.Error(err)
+				return
 			}
 		}()
 
 		wg.Wait()
 	}
 
-	run_test(true, false)
-	run_test(false, false)
-	run_test(true, true)
-	run_test(false, true)
+	t.Run("close TCP, server reads", func(t *testing.T) {
+		run_test(t, true, false)
+	})
+	t.Run("close SSL, server reads", func(t *testing.T) {
+		run_test(t, false, false)
+	})
+	t.Run("close TCP, server writes", func(t *testing.T) {
+		run_test(t, true, true)
+	})
+	t.Run("close SSL, server writes", func(t *testing.T) {
+		run_test(t, false, true)
+	})
 }
 
 func ThroughputBenchmark(b *testing.B, constructor func(