diff --git a/igzip/data_struct2.asm b/igzip/data_struct2.asm
index b5cd659..abca975 100644
--- a/igzip/data_struct2.asm
+++ b/igzip/data_struct2.asm
@@ -82,7 +82,7 @@ FIELD   _tmp_out_start,	4,	4
 FIELD	_tmp_out_end,	4,	4
 FIELD	_has_eob,		4,	4
 FIELD	_has_eob_hdr,	4,	4
-FIELD	_left_over, 4,	4
+FIELD	_has_hist, 4,	4
 FIELD	_buffer,	BSIZE,	32
 FIELD	_head,		IGZIP_HASH_SIZE*2,	16
 
@@ -129,7 +129,7 @@ _internal_state_tmp_out_start		  equ   _internal_state+_tmp_out_start
 _internal_state_tmp_out_end		  equ   _internal_state+_tmp_out_end
 _internal_state_has_eob		  equ   _internal_state+_has_eob
 _internal_state_has_eob_hdr		  equ   _internal_state+_has_eob_hdr
-_internal_state_left_over		  equ   _internal_state+_left_over
+_internal_state_has_hist		  equ   _internal_state+_has_hist
 _internal_state_buffer			  equ   _internal_state+_buffer
 _internal_state_head			  equ   _internal_state+_head
 _internal_state_bitbuf_m_bits		  equ   _internal_state+_bitbuf_m_bits
diff --git a/igzip/igzip.c b/igzip/igzip.c
index 88afd23..ad12d2b 100644
--- a/igzip/igzip.c
+++ b/igzip/igzip.c
@@ -526,6 +526,8 @@ static inline void reset_match_history(struct isal_zstream *stream)
 	uint16_t *head = stream->internal_state.head;
 	int i = 0;
 
+	state->has_hist = 0;
+
 	if (stream->total_in == 0)
 		memset(stream->internal_state.head, 0, sizeof(stream->internal_state.head));
 	else {
@@ -549,7 +551,7 @@ void isal_deflate_init(struct isal_zstream *stream)
 	state->b_bytes_processed = 0;
 	state->has_eob = 0;
 	state->has_eob_hdr = 0;
-	state->left_over = 0;
+	state->has_hist = 0;
 	state->state = ZSTATE_NEW_HDR;
 	state->count = 0;
 
diff --git a/igzip/igzip_body.asm b/igzip/igzip_body.asm
index e325ee2..e588af6 100644
--- a/igzip/igzip_body.asm
+++ b/igzip/igzip_body.asm
@@ -199,31 +199,23 @@ skip1:
 
 	; for (f_i = f_start_i; f_i < f_end_i; f_i++) {
 MARK __body_compute_hash_ %+ ARCH
+	MOVDQU	xdata, [file_start + f_i]
 	mov	curr_data, [file_start + f_i]
+	mov	tmp3, curr_data
+	mov	tmp6, curr_data
 
-	cmp	m_out_buf, [stream + _internal_state_bitbuf_m_out_end]
-	ja	output_end
-
-	;; Encode first byte in the stream as a literal
 	compute_hash	hash, curr_data
-	and	hash %+ d, HASH_MASK
-	mov	[stream + _internal_state_head + 2 * hash], f_i %+ w
-	and	curr_data, 0xff
-	get_lit_code	curr_data, code2, code_len2, hufftables
 
-	mov	tmp3, [file_start + f_i + 1]
-	mov	tmp6, tmp3
-	compute_hash	hash, tmp3
+	shr	tmp3, 8
+	compute_hash	hash2, tmp3
 
-	shr	tmp6, 8
-	compute_hash	hash2, tmp6
+	and	hash, HASH_MASK
+	and	hash2, HASH_MASK
 
-	MOVD	xhash, hash %+ d
-	PINSRD	xhash, hash2 %+ d, 1
-	PAND	xhash, xhash, xmask
-
-	jmp	write_lit_bits
+	cmp	dword [stream + _internal_state_has_hist], 0
+	je	write_first_byte
 
+	jmp	loop2
 	align	16
 
 loop2:
@@ -548,6 +540,27 @@ compare_loop2:
 	get_lit_code	curr_data, code3, code_len3, hufftables
 	jmp	len_dist_lit_huffman
 
+MARK __write_first_byte_ %+ ARCH
+write_first_byte:
+	cmp	m_out_buf, [stream + _internal_state_bitbuf_m_out_end]
+	ja	output_end
+
+	mov	dword [stream + _internal_state_has_hist], 1
+
+	mov	[stream + _internal_state_head + 2 * hash], f_i %+ w
+
+	mov	hash, hash2
+	shr	tmp6, 16
+	compute_hash	hash2, tmp6
+
+	MOVD	xhash, hash %+ d
+	PINSRD	xhash, hash2 %+ d, 1
+	PAND	xhash, xhash, xmask
+
+	and	curr_data, 0xff
+	get_lit_code	curr_data, code2, code_len2, hufftables
+	jmp	write_lit_bits
+
 section .data
 	align 16
 mask:	dd	HASH_MASK, HASH_MASK, HASH_MASK, HASH_MASK
diff --git a/igzip/igzip_finish.asm b/igzip/igzip_finish.asm
index 9b93e25..e8d5e36 100644
--- a/igzip/igzip_finish.asm
+++ b/igzip/igzip_finish.asm
@@ -126,7 +126,7 @@ skip_SLOP:
 
 	mov	curr_data %+ d, [file_start + f_i]
 
-	cmp	dword [stream + _internal_state_b_bytes_processed], 0 ;TODO fixz
+	cmp	dword [stream + _internal_state_has_hist], 0
 	jne	skip_write_first_byte
 
 	cmp	m_out_buf, [stream + _internal_state_bitbuf_m_out_end]
@@ -135,6 +135,7 @@ skip_SLOP:
 	compute_hash	hash, curr_data
 	and	hash %+ d, HASH_MASK
 	mov	[stream + _internal_state_head + 2 * hash], f_i %+ w
+	mov	dword [stream + _internal_state_has_hist], 1
 	jmp	encode_literal
 
 skip_write_first_byte:
diff --git a/include/igzip_lib.h b/include/igzip_lib.h
index 147f931..781d026 100644
--- a/include/igzip_lib.h
+++ b/include/igzip_lib.h
@@ -240,7 +240,7 @@ struct isal_zstate {
 	uint32_t tmp_out_end;	//!< temporary variable
 	uint32_t has_eob;	//!< keeps track of eob on the last deflate block
 	uint32_t has_eob_hdr;	//!< keeps track of eob hdr (with BFINAL set)
-	uint32_t left_over;	//!< keeps track of overflow bytes
+	uint32_t has_hist;	//!< flag to track if there is match history
 
 	DECLARE_ALIGNED(uint8_t buffer[2 * IGZIP_HIST_SIZE + ISAL_LOOK_AHEAD], 32);	//!< Internal buffer
 	DECLARE_ALIGNED(uint16_t head[IGZIP_HASH_SIZE], 16);	//!< Hash array