diff --git a/crypto/sha/asm/sha256-586.pl b/crypto/sha/asm/sha256-586.pl
index 8fe13bc5336fcc3108892e394edc48b39e8d50ef..4cc1576b8968420591cb11dfd7b5bd390111be53 100644
--- a/crypto/sha/asm/sha256-586.pl
+++ b/crypto/sha/asm/sha256-586.pl
@@ -45,13 +45,17 @@ $Xoff=&DWP(32,"esp");
 $K256="ebp";
 
 sub BODY_00_15() {
+    my $in_16_64=shift;
+
 	&mov	("ecx",$E);
+	 &add	($T,&DWP(4*(8+15+16-9),"esp"))	if ($in_16_64);	# T += X[-7]
 	&ror	("ecx",6);
 	&mov	("edi",$E);
 	&ror	("edi",11);
 	 &mov	("esi",$Foff);
 	&xor	("ecx","edi");
 	&ror	("edi",25-11);
+	 &mov	(&DWP(4*(8+15),"esp"),$T)	if ($in_16_64);	# save X[0]
 	&xor	("ecx","edi");	# Sigma1(e)
 	 &mov	("edi",$Goff);
 	&add	($T,"ecx");	# T += Sigma1(e)
@@ -88,6 +92,7 @@ sub BODY_00_15() {
 
 	&add	($K256,4);
 	&add	($A,$T);	# h += T
+	 &mov	($T,&DWP(4*(8+15+16-1),"esp"))	if ($in_16_64);	# preload T
 	&add	($E,"esi");	# d += K256[i]
 	&add	($A,"esi");	# h += K256[i]
 }
@@ -159,10 +164,10 @@ sub BODY_00_15() {
 	&cmp	("esi",0xc19bf174);
 	&jne	(&label("00_15"));
 
+	&mov	($T,&DWP(4*(8+15+16-1),"esp"));	# preloaded in BODY_00_15(1)
 &set_label("16_63",16);
-	&mov	($T,&DWP(4*(8+15+16-1),"esp"));
-	 &mov	("ecx",&DWP(4*(8+15+16-14),"esp"));
 	&mov	("esi",$T);
+	 &mov	("ecx",&DWP(4*(8+15+16-14),"esp"));
 	&shr	($T,3);
 	&ror	("esi",7);
 	&xor	($T,"esi");
@@ -176,13 +181,13 @@ sub BODY_00_15() {
 	&xor	("ecx","edi");
 	&ror	("edi",19-17);
 	 &add	($T,"esi");			# T += X[-16]
-	&xor	("ecx","edi")			# sigma1(X[-2])
+	&xor	("edi","ecx")			# sigma1(X[-2])
 
-	&add	($T,"ecx");			# T += sigma1(X[-2])
-	&add	($T,&DWP(4*(8+15+16-9),"esp"));	# T += X[-7]
-	&mov	(&DWP(4*(8+15),"esp"),$T);	# save X[0]
+	&add	($T,"edi");			# T += sigma1(X[-2])
+	# &add	($T,&DWP(4*(8+15+16-9),"esp"));	# T += X[-7], moved to BODY_00_15(1)
+	# &mov	(&DWP(4*(8+15),"esp"),$T);	# save X[0]
 
-	&BODY_00_15();
+	&BODY_00_15(1);
 
 	&cmp	("esi",0xc67178f2);
 	&jne	(&label("16_63"));
diff --git a/crypto/sha/asm/sha512-586.pl b/crypto/sha/asm/sha512-586.pl
index 49a981454494072b7e73e9b8e17d306c43fedaea..5554f022e99b777cfadeb739cee708e0096ddcbd 100644
--- a/crypto/sha/asm/sha512-586.pl
+++ b/crypto/sha/asm/sha512-586.pl
@@ -68,6 +68,8 @@ $E="mm4";	# F-H are commonly loaded to respectively mm1-mm3 and
 		# mm5-mm7, but it's done on on-demand basis...
 
 sub BODY_00_15_sse2 {
+    my $prefetch=shift;
+
 	&movq	("mm5",$Fsse2);			# load f
 	&movq	("mm6",$Gsse2);			# load g
 	&movq	("mm7",$Hsse2);			# load h
@@ -96,7 +98,7 @@ sub BODY_00_15_sse2 {
 	&pxor	("mm5","mm6");			# f^=g
 	&movq	($E,$Dsse2);			# e = load d
 	&paddq	("mm3","mm5");			# T1+=Ch(e,f,g)
-
+	&movq	(&QWP(0,"esp"),$A);		# modulo-scheduled save a
 	&paddq	("mm3","mm7");			# T1+=h
 
 	&movq	("mm5",$A);			# %mm5 is sliding right
@@ -114,15 +116,16 @@ sub BODY_00_15_sse2 {
 	&pxor	("mm7","mm6");
 	&psllq	("mm6",6);
 	&pxor	("mm7","mm5");
-	&movq	(&QWP(0,"esp"),$A);		# modulo-scheduled save a
+	&sub	("esp",8);
 	&pxor	("mm7","mm6");			# T2=Sigma0_512(a)
 
 	&movq	("mm5",$A);			# %mm5=a
 	&por	($A,"mm2");			# a=a|c
+	&movq	("mm6",&QWP(8*(9+16-14),"esp"))	if ($prefetch);
 	&pand	("mm5","mm2");			# %mm5=a&c
 	&pand	($A,"mm1");			# a=(a|c)&b
+	&movq	("mm2",&QWP(8*(9+16-1),"esp"))	if ($prefetch);
 	&por	("mm5",$A);			# %mm5=(a&c)|((a|c)&b)
-	&sub	("esp",8);
 	&paddq	("mm7","mm5");			# T2+=Maj(a,b,c)
 	&movq	($A,"mm3");			# a=T1
 
@@ -327,48 +330,48 @@ if ($sse2) {
 	&cmp	(&LB("edx"),0x35);
 	&jne	(&label("00_14_sse2"));
 
-	&BODY_00_15_sse2();
+	&BODY_00_15_sse2(1);
 
 &set_label("16_79_sse2",16);
-	&movq	("mm3",&QWP(8*(9+16-1),"esp"));
-	&movq	("mm6",&QWP(8*(9+16-14),"esp"));
-	&movq	("mm1","mm3");
+	#&movq	("mm2",&QWP(8*(9+16-1),"esp"));	#prefetched in BODY_00_15 
+	#&movq	("mm6",&QWP(8*(9+16-14),"esp"));
+	&movq	("mm1","mm2");
 
-	&psrlq	("mm3",1);
+	&psrlq	("mm2",1);
 	&movq	("mm7","mm6");
 	&psrlq	("mm6",6);
-	&movq	("mm2","mm3");
+	&movq	("mm3","mm2");
 
-	&psrlq	("mm3",7-1);
+	&psrlq	("mm2",7-1);
 	&movq	("mm5","mm6");
 	&psrlq	("mm6",19-6);
-	&pxor	("mm2","mm3");
+	&pxor	("mm3","mm2");
 
-	&psrlq	("mm3",8-7);
+	&psrlq	("mm2",8-7);
 	&pxor	("mm5","mm6");
 	&psrlq	("mm6",61-19);
-	&pxor	("mm2","mm3");
+	&pxor	("mm3","mm2");
 
-	&movq	("mm3",&QWP(8*(9+16),"esp"));
+	&movq	("mm2",&QWP(8*(9+16),"esp"));
 
 	&psllq	("mm1",56);
 	&pxor	("mm5","mm6");
 	&psllq	("mm7",3);
-	&pxor	("mm2","mm1");
+	&pxor	("mm3","mm1");
 
-	&paddq	("mm3",&QWP(8*(9+16-9),"esp"));
+	&paddq	("mm2",&QWP(8*(9+16-9),"esp"));
 
 	&psllq	("mm1",63-56);
 	&pxor	("mm5","mm7");
 	&psllq	("mm7",45-3);
-	&pxor	("mm2","mm1");
+	&pxor	("mm3","mm1");
 	&pxor	("mm5","mm7");
 
-	&paddq	("mm2","mm5");
-	&paddq	("mm2","mm3");
-	&movq	(&QWP(8*9,"esp"),"mm2");
+	&paddq	("mm3","mm5");
+	&paddq	("mm3","mm2");
+	&movq	(&QWP(8*9,"esp"),"mm3");
 
-	&BODY_00_15_sse2();
+	&BODY_00_15_sse2(1);
 
 	&cmp	(&LB("edx"),0x17);
 	&jne	(&label("16_79_sse2"));