diff --git a/apps/zasm/instr.asm b/apps/zasm/instr.asm
index ee064ae..f070c93 100644
--- a/apps/zasm/instr.asm
+++ b/apps/zasm/instr.asm
@@ -615,22 +615,57 @@ getUpcode:
 	ld	c, 1
 	jr	.computeBytesWritten
 .withByte:
-	; verify that the MSB in argument is zero
 	inc	hl
+	; HL points to our number (LSB), with (HL+1) being our MSB which should
+	; normally by zero. However, if our instruction is jr or djnz, that
+	; number is actually a 2-bytes address that has to be relative to PC,
+	; so it's a special case. Let's check for this special case.
+	bit	7, (ix+3)
+	jr	z, .absoluteValue	; bit not set? regular byte value,
+	; Our argument is a relative address ("e" type in djnz and jr). We have
+	; to subtract (curOutputOffset) from it.
+
+	; First, check whether we're on first pass. If we are, skip processing
+	; below because not having real symbol value makes relative address
+	; verification falsely fail.
+	ld	c, 2	; this is a two bytes instruction
+	call	zasmIsFirstPass
+	jr	z, .computeBytesWritten
+
+	; We're on second pass
+	push	de		; Don't let go of this, that's our dest
+	ld	de, (curOutputOffset)
+	call	JUMP_INTOHL
+	dec	hl		; what we write is "e-2"
+	dec	hl
+	call	subDEFromHL
+	pop	de		; Still have it? good
+	; HL contains our number and we'll check its bounds. If It's negative,
+	; H is going to be 0xff and L has to be >= 0x80. If it's positive,
+	; H is going to be 0 and L has to be < 0x80.
+	ld	a, l
+	cp	0x80
+	jr	c, .skipHInc	; a < 0x80, H is expected to be 0
+	; A being >= 0x80 is only valid in cases where HL is negative and
+	; within bounds. This only happens is H == 0xff. Let's increase it to 0.
+	inc	h
+.skipHInc:
+	; Let's write our value now even though we haven't checked our bounds
+	; yet. This way, we don't have to store A somewhere else.
+	ld	(de), a
+	ld	a, h
+	or	a		; cp 0
+	jr	nz, .numberTruncated	; if A is anything but zero, we're out
+					; of bounds.
+	jr	.computeBytesWritten
+
+.absoluteValue:
+	; verify that the MSB in argument is zero
 	inc	hl	; MSB is 2nd byte
 	ld	a, (hl)
 	dec	hl	; HL now points to LSB
 	or	a	; cp 0
 	jr	nz, .numberTruncated
-	; HL points to our number
-	; one last thing to check. Is the 7th bit on the displacement value set?
-	; if yes, we have to decrease our value by 2. Uses for djnz and jr.
-	bit	7, (ix+3)
-	jr	z, .skipDecrease
-	; Yup, it's set.
-	dec	(hl)
-	dec	(hl)
-.skipDecrease:
 	ldi
 	ld	c, 2
 	jr	.computeBytesWritten
diff --git a/apps/zasm/main.asm b/apps/zasm/main.asm
index 6f05dce..af5e285 100644
--- a/apps/zasm/main.asm
+++ b/apps/zasm/main.asm
@@ -25,6 +25,7 @@
 ; JUMP_UPCASE
 ; JUMP_UNSETZ
 ; JUMP_INTODE
+; JUMP_INTOHL
 ; JUMP_FINDCHAR
 ; JUMP_BLKSEL
 ; RAMSTART	(where we put our variables in RAM)
diff --git a/apps/zasm/tests/test2.asm b/apps/zasm/tests/test2.asm
new file mode 100644
index 0000000..744982f
--- /dev/null
+++ b/apps/zasm/tests/test2.asm
@@ -0,0 +1,11 @@
+; Test relative jumps
+label1:
+	jp	label1
+	jp	label2
+	jp	label2
+	jr	label2
+	jr	nc, label1
+
+label2:
+	jr	label1
+	jr	nc, label1
diff --git a/apps/zasm/util.asm b/apps/zasm/util.asm
index b0c598d..74a9938 100644
--- a/apps/zasm/util.asm
+++ b/apps/zasm/util.asm
@@ -22,6 +22,18 @@ cpHLDE:
 	cp	e
 	ret		; flags are correct
 
+; HL - DE -> HL
+subDEFromHL:
+	push	af
+	ld	a, l
+	sub	e
+	ld	l, a
+	ld	a, h
+	sbc	d
+	ld	h, a
+	pop	af
+	ret
+
 ; Returns length of string at (HL) in A.
 strlen:
 	push	bc
diff --git a/tools/emul/zasm.c b/tools/emul/zasm.c
index 891bcf4..d087174 100644
--- a/tools/emul/zasm.c
+++ b/tools/emul/zasm.c
@@ -33,6 +33,7 @@
 #define STDIN_BUFSIZE 0x8000
 // When defined, we dump memory instead of dumping expected stdout
 //#define MEMDUMP
+//#define DEBUG
 
 static Z80Context cpu;
 static uint8_t mem[0x10000];
@@ -119,7 +120,9 @@ int main()
     }
 #endif
     fflush(stdout);
+#ifdef DEBUG
     fprintf(stderr, "Ended with A=%d DE=%d\n", cpu.R1.br.A, cpu.R1.wr.DE);
+#endif
     return 0;
 }
 
diff --git a/tools/emul/zasm_glue.asm b/tools/emul/zasm_glue.asm
index 5dce484..c1b48b1 100644
--- a/tools/emul/zasm_glue.asm
+++ b/tools/emul/zasm_glue.asm
@@ -12,6 +12,7 @@ jp	addHL
 jp	upcase
 jp	unsetZ
 jp	intoDE
+jp	intoHL
 jp	findchar
 jp	parseHexPair
 jp	blkSel
diff --git a/tools/emul/zasm_user.asm b/tools/emul/zasm_user.asm
index 3224e16..ff78e2f 100644
--- a/tools/emul/zasm_user.asm
+++ b/tools/emul/zasm_user.asm
@@ -5,9 +5,10 @@ JUMP_ADDHL      .equ    0x08
 JUMP_UPCASE     .equ    0x0b
 JUMP_UNSETZ     .equ    0x0e
 JUMP_INTODE	.equ    0x11
-JUMP_FINDCHAR	.equ    0x14
-JUMP_PARSEHEXPAIR .equ    0x17
-JUMP_BLKSEL	.equ    0x1a
+JUMP_INTOHL	.equ    0x14
+JUMP_FINDCHAR	.equ    0x17
+JUMP_PARSEHEXPAIR .equ    0x1a
+JUMP_BLKSEL	.equ    0x1d
 
 .equ	USER_CODE	0x4800
 .equ	RAMSTART	0x5800