diff --git a/101screen.subx b/101screen.subx
index 2aab293d..b957d5d2 100644
--- a/101screen.subx
+++ b/101screen.subx
@@ -6,6 +6,19 @@
 == code
 
 pixel-on-real-screen:  # x: int, y: int, color: int
+    # . prologue
+    55/push-ebp
+    89/<- %ebp 4/r32/esp
+    #
+    (pixel-on-screen-buffer *Video-memory-addr *(ebp+8) *(ebp+0xc) *(ebp+0x10) 0x400 0x300)
+$pixel-on-real-screen:end:
+    # . epilogue
+    89/<- %esp 5/r32/ebp
+    5d/pop-to-ebp
+    c3/return
+
+# 'buffer' here is not a valid Mu type: a naked address without a length.
+pixel-on-screen-buffer:  # buffer: (addr byte), x: int, y: int, color: int, width: int, height: int
     # . prologue
     55/push-ebp
     89/<- %ebp 4/r32/esp
@@ -13,26 +26,26 @@ pixel-on-real-screen:  # x: int, y: int, color: int
     50/push-eax
     51/push-ecx
     # bounds checks
-    8b/-> *(ebp+8) 0/r32/eax
+    8b/-> *(ebp+0xc) 0/r32/eax  # foo
     3d/compare-eax-and 0/imm32
-    7c/jump-if-< $pixel-on-real-screen:end/disp8
-    3d/compare-eax-and 0x400/imm32/screen-width=1024
-    7d/jump-if->= $pixel-on-real-screen:end/disp8
-    8b/-> *(ebp+0xc) 0/r32/eax
+    7c/jump-if-< $pixel-on-screen-buffer:end/disp8
+    3b/compare 0/r32/eax *(ebp+0x18)
+    7d/jump-if->= $pixel-on-screen-buffer:end/disp8
+    8b/-> *(ebp+0x10) 0/r32/eax
     3d/compare-eax-and 0/imm32
-    7c/jump-if-< $pixel-on-real-screen:end/disp8
-    3d/compare-eax-and 0x300/imm32/screen-height=768
-    7d/jump-if->= $pixel-on-real-screen:end/disp8
-    # eax = y*1024 + x
-    8b/-> *(ebp+0xc) 0/r32/eax
-    c1/shift 4/subop/left %eax 0xa/imm8
-    03/add-> *(ebp+8) 0/r32/eax
+    7c/jump-if-< $pixel-on-screen-buffer:end/disp8
+    3b/compare 0/r32/eax *(ebp+0x1c)
+    7d/jump-if->= $pixel-on-screen-buffer:end/disp8
+    # eax = y*width + x
+    8b/-> *(ebp+0x10) 0/r32/eax
+    0f af/multiply-> *(ebp+0x18) 0/r32/eax
+    03/add-> *(ebp+0xc) 0/r32/eax
     # eax += location of frame buffer
-    03/add-> *Video-memory-addr 0/r32/eax
+    03/add-> *(ebp+8) 0/r32/eax
     # *eax = color
-    8b/-> *(ebp+0x10) 1/r32/ecx
+    8b/-> *(ebp+0x14) 1/r32/ecx
     88/byte<- *eax 1/r32/CL
-$pixel-on-real-screen:end:
+$pixel-on-screen-buffer:end:
     # . restore registers
     59/pop-to-ecx
     58/pop-to-eax
diff --git a/103grapheme.subx b/103grapheme.subx
index 8f1f9e61..ac0cef95 100644
--- a/103grapheme.subx
+++ b/103grapheme.subx
@@ -15,6 +15,21 @@
 # Doesn't update the cursor; where the cursor should go after printing the
 # current grapheme is a higher-level concern.
 draw-grapheme-on-real-screen:  # g: grapheme, x: int, y: int, color: int, background-color: int
+    # . prologue
+    55/push-ebp
+    89/<- %ebp 4/r32/esp
+    #
+    (draw-grapheme-on-screen-buffer *Video-memory-addr *(ebp+8) *(ebp+0xc) *(ebp+0x10) *(ebp+0x14) *(ebp+0x18) 0x400 0x300)
+$draw-grapheme-on-real-screen:end:
+    # . epilogue
+    89/<- %esp 5/r32/ebp
+    5d/pop-to-ebp
+    c3/return
+
+# 'buffer' here is not a valid Mu type: a naked address without a length.
+# 'x' and 'y' are in graphemes
+# 'screen-width' and 'screen-height' are in pixels
+draw-grapheme-on-screen-buffer:  # buffer: (addr byte), g: grapheme, x: int, y: int, color: int, background-color: int, screen-width: int, screen-height: int
     # . prologue
     55/push-ebp
     89/<- %ebp 4/r32/esp
@@ -25,30 +40,30 @@ draw-grapheme-on-real-screen:  # g: grapheme, x: int, y: int, color: int, backgr
     53/push-ebx
     56/push-esi
     # esi = g
-    8b/-> *(ebp+8) 6/r32/esi
+    8b/-> *(ebp+0xc) 6/r32/esi
     # if (g >= 128) return  # characters beyond ASCII currently not supported
     81 7/subop/compare %esi 0x80/imm32
-    7d/jump-if->= $draw-grapheme-on-real-screen:end/disp8
+    0f 8d/jump-if->= $draw-grapheme-on-screen-buffer:end/disp32
     # var letter-bitmap/esi = font[g]
     c1 4/subop/shift-left %esi 4/imm8
     81 0/subop/add %esi Font/imm32
     # var ycurr/edx: int = y*16
-    8b/-> *(ebp+0x10) 2/r32/edx
+    8b/-> *(ebp+0x14) 2/r32/edx
     c1 4/subop/shift-left %edx 4/imm8
     # var ymax/ebx: int = ycurr + 16
-    8b/-> *(ebp+0x10) 3/r32/ebx
+    8b/-> *(ebp+0x14) 3/r32/ebx
     c1 4/subop/shift-left %ebx 4/imm8
     81 0/subop/add %ebx 0x10/imm32
     {
       # if (ycurr >= ymax) break
       39/compare %edx 3/r32/ebx
-      7d/jump-if->= break/disp8
+      0f 8d/jump-if->= break/disp32
       # var xcurr/eax: int = x*8 + 7
-      8b/-> *(ebp+0xc) 0/r32/eax  # font-width - 1
+      8b/-> *(ebp+0x10) 0/r32/eax  # font-width - 1
       c1 4/subop/shift-left %eax 3/imm8
       05/add-to-eax 7/imm32
       # var xmin/ecx: int = x*8
-      8b/-> *(ebp+0xc) 1/r32/ecx
+      8b/-> *(ebp+0x10) 1/r32/ecx
       c1 4/subop/shift-left %ecx 3/imm8
       # var row-bitmap/ebx: int = *letter-bitmap
       53/push-ebx
@@ -62,12 +77,12 @@ draw-grapheme-on-real-screen:  # g: grapheme, x: int, y: int, color: int, backgr
         # if LSB, draw a pixel in the given color
         {
           73/jump-if-not-CF break/disp8
-          (pixel-on-real-screen %eax %edx *(ebp+0x14))
-          eb/jump $draw-grapheme-on-real-screen:continue/disp8
+          (pixel-on-screen-buffer *(ebp+8) %eax %edx *(ebp+0x18) *(ebp+0x20) *(ebp+0x24))
+          eb/jump $draw-grapheme-on-screen-buffer:continue/disp8
         }
         # otherwise use the background color
-        (pixel-on-real-screen %eax %edx *(ebp+0x18))
-$draw-grapheme-on-real-screen:continue:
+        (pixel-on-screen-buffer *(ebp+8) %eax %edx *(ebp+0x1c) *(ebp+0x20) *(ebp+0x24))
+$draw-grapheme-on-screen-buffer:continue:
         # --x
         48/decrement-eax
         #
@@ -80,9 +95,9 @@ $draw-grapheme-on-real-screen:continue:
       # next bitmap row
       46/increment-esi
       #
-      eb/jump loop/disp8
+      e9/jump loop/disp32
     }
-$draw-grapheme-on-real-screen:end:
+$draw-grapheme-on-screen-buffer:end:
     # . restore registers
     5e/pop-to-esi
     5b/pop-to-ebx