diff --git a/chacha20/chacha_generic.go b/chacha20/chacha_generic.go
index 18c8bc0..a2ecf5c 100644
--- a/chacha20/chacha_generic.go
+++ b/chacha20/chacha_generic.go
@@ -42,10 +42,14 @@
 
 	// The last len bytes of buf are leftover key stream bytes from the previous
 	// XORKeyStream invocation. The size of buf depends on how many blocks are
-	// computed at a time.
+	// computed at a time by xorKeyStreamBlocks.
 	buf [bufSize]byte
 	len int
 
+	// overflow is set when the counter overflowed, no more blocks can be
+	// generated, and the next XORKeyStream call should panic.
+	overflow bool
+
 	// The counter-independent results of the first round are cached after they
 	// are computed the first time.
 	precompDone      bool
@@ -140,15 +144,18 @@
 // SetCounter sets the Cipher counter. The next invocation of XORKeyStream will
 // behave as if (64 * counter) bytes had been encrypted so far.
 //
-// To prevent accidental counter reuse, SetCounter panics if counter is
-// less than the current value.
+// To prevent accidental counter reuse, SetCounter panics if counter is less
+// than the current value.
+//
+// Note that the execution time of XORKeyStream is not independent of the
+// counter value.
 func (s *Cipher) SetCounter(counter uint32) {
 	// Internally, s may buffer multiple blocks, which complicates this
 	// implementation slightly. When checking whether the counter has rolled
 	// back, we must use both s.counter and s.len to determine how many blocks
 	// we have already output.
 	outputCounter := s.counter - uint32(s.len)/blockSize
-	if counter < outputCounter {
+	if s.overflow || counter < outputCounter {
 		panic("chacha20: SetCounter attempted to rollback counter")
 	}
 
@@ -197,34 +204,52 @@
 			dst[i] = src[i] ^ b
 		}
 		s.len -= len(keyStream)
-		src = src[len(keyStream):]
-		dst = dst[len(keyStream):]
+		dst, src = dst[len(keyStream):], src[len(keyStream):]
+	}
+	if len(src) == 0 {
+		return
 	}
 
-	const blocksPerBuf = bufSize / blockSize
-	numBufs := (uint64(len(src)) + bufSize - 1) / bufSize
-	if uint64(s.counter)+numBufs*blocksPerBuf >= 1<<32 {
+	// If we'd need to let the counter overflow and keep generating output,
+	// panic immediately. If instead we'd only reach the last block, remember
+	// not to generate any more output after the buffer is drained.
+	numBlocks := (uint64(len(src)) + blockSize - 1) / blockSize
+	if s.overflow || uint64(s.counter)+numBlocks > 1<<32 {
 		panic("chacha20: counter overflow")
+	} else if uint64(s.counter)+numBlocks == 1<<32 {
+		s.overflow = true
 	}
 
 	// xorKeyStreamBlocks implementations expect input lengths that are a
 	// multiple of bufSize. Platform-specific ones process multiple blocks at a
 	// time, so have bufSizes that are a multiple of blockSize.
 
-	rem := len(src) % bufSize
-	full := len(src) - rem
-
+	full := len(src) - len(src)%bufSize
 	if full > 0 {
 		s.xorKeyStreamBlocks(dst[:full], src[:full])
 	}
+	dst, src = dst[full:], src[full:]
+
+	// If using a multi-block xorKeyStreamBlocks would overflow, use the generic
+	// one that does one block at a time.
+	const blocksPerBuf = bufSize / blockSize
+	if uint64(s.counter)+blocksPerBuf > 1<<32 {
+		s.buf = [bufSize]byte{}
+		numBlocks := (len(src) + blockSize - 1) / blockSize
+		buf := s.buf[bufSize-numBlocks*blockSize:]
+		copy(buf, src)
+		s.xorKeyStreamBlocksGeneric(buf, buf)
+		s.len = len(buf) - copy(dst, buf)
+		return
+	}
 
 	// If we have a partial (multi-)block, pad it for xorKeyStreamBlocks, and
 	// keep the leftover keystream for the next XORKeyStream invocation.
-	if rem > 0 {
+	if len(src) > 0 {
 		s.buf = [bufSize]byte{}
-		copy(s.buf[:], src[full:])
+		copy(s.buf[:], src)
 		s.xorKeyStreamBlocks(s.buf[:], s.buf[:])
-		s.len = bufSize - copy(dst[full:], s.buf[:])
+		s.len = bufSize - copy(dst, s.buf[:])
 	}
 }
 
@@ -308,9 +333,6 @@
 		addXor(dst[60:64], src[60:64], x15, c15)
 
 		s.counter += 1
-		if s.counter == 0 {
-			panic("chacha20: internal error: counter overflow")
-		}
 
 		src, dst = src[blockSize:], dst[blockSize:]
 	}
diff --git a/chacha20/chacha_test.go b/chacha20/chacha_test.go
index 554afbf..d75873c 100644
--- a/chacha20/chacha_test.go
+++ b/chacha20/chacha_test.go
@@ -148,11 +148,66 @@
 	if !panics(func() { s.SetCounter(0) }) {
 		t.Error("counter decreasing should trigger a panic")
 	}
-	// advancing to ^uint32(0) and then calling XORKeyStream should cause a panic
-	s = newCipher()
-	s.SetCounter(^uint32(0))
-	if !panics(func() { s.XORKeyStream([]byte{0}, []byte{0}) }) {
-		t.Error("counter overflowing should trigger a panic")
+}
+
+func TestLastBlock(t *testing.T) {
+	panics := func(fn func()) (p bool) {
+		defer func() { p = recover() != nil }()
+		fn()
+		return
+	}
+
+	checkLastBlock := func(b []byte) {
+		t.Helper()
+		// Hardcoded result to check all implementations generate the same output.
+		lastBlock := "ace4cd09e294d1912d4ad205d06f95d9c2f2bfcf453e8753f128765b62215f4d" +
+			"92c74f2f626c6a640c0b1284d839ec81f1696281dafc3e684593937023b58b1d"
+		if got := hex.EncodeToString(b); got != lastBlock {
+			t.Errorf("wrong output for the last block, got %q, want %q", got, lastBlock)
+		}
+	}
+
+	// setting the counter to 0xffffffff and crypting multiple blocks should
+	// trigger a panic
+	s, _ := NewUnauthenticatedCipher(make([]byte, KeySize), make([]byte, NonceSize))
+	s.SetCounter(0xffffffff)
+	blocks := make([]byte, blockSize*2)
+	if !panics(func() { s.XORKeyStream(blocks, blocks) }) {
+		t.Error("crypting multiple blocks should trigger a panic")
+	}
+
+	// setting the counter to 0xffffffff - 1 and crypting two blocks should not
+	// trigger a panic
+	s, _ = NewUnauthenticatedCipher(make([]byte, KeySize), make([]byte, NonceSize))
+	s.SetCounter(0xffffffff - 1)
+	if panics(func() { s.XORKeyStream(blocks, blocks) }) {
+		t.Error("crypting the last blocks should not trigger a panic")
+	}
+	checkLastBlock(blocks[blockSize:])
+	// once all the keystream is spent, setting the counter should panic
+	if !panics(func() { s.SetCounter(0xffffffff) }) {
+		t.Error("setting the counter after overflow should trigger a panic")
+	}
+	// crypting a subsequent block *should* panic
+	block := make([]byte, blockSize)
+	if !panics(func() { s.XORKeyStream(block, block) }) {
+		t.Error("crypting after overflow should trigger a panic")
+	}
+
+	// if we crypt less than a full block, we should be able to crypt the rest
+	// in a subsequent call without panicking
+	s, _ = NewUnauthenticatedCipher(make([]byte, KeySize), make([]byte, NonceSize))
+	s.SetCounter(0xffffffff)
+	if panics(func() { s.XORKeyStream(block[:7], block[:7]) }) {
+		t.Error("crypting part of the last block should not trigger a panic")
+	}
+	if panics(func() { s.XORKeyStream(block[7:], block[7:]) }) {
+		t.Error("crypting part of the last block should not trigger a panic")
+	}
+	checkLastBlock(block)
+	// as before, a third call should trigger a panic because all keystream is spent
+	if !panics(func() { s.XORKeyStream(block[:1], block[:1]) }) {
+		t.Error("crypting after overflow should trigger a panic")
 	}
 }