For those of us who may not be quite as proficient with Linux - here is a little more detail (I just struggled through this tonight for about an hour myself and this bug helped me 80% of the way).

In your /var/log/Xorg.0.log file, look for the following lines:

.
.
(II) GLINT(0): Printing DDC gathered Modelines:
(II) GLINT(0): Modeline "800x600"   40.00  800 840 968 1056  600 601 605 628 +hsync +vsync
(II) GLINT(0): Modeline "800x600"   36.00  800 824 896 1024  600 601 603 625 +hsync +vsync
.
.etc..


Copy all of these "Modelines" entries into the "Monitor" section of your /etc/X11/xorg.conf file, removing the "(II) GLINT(0): " part.  For example, now the Monitor section of your xorg.conf file may look like this:

Section "Monitor"
	Identifier	"NEC FE950+"
	Option		"DPMS"
	Modeline "800x600"   40.00  800 840 968 1056  600 601 605 628 +hsync +vsync
	Modeline "800x600"   36.00  800 824 896 1024  600 601 603 625 +hsync +vsync
	.
	.etc.
EndSection

However!  This still did not work for me.  I was not given any other resolution options after restarting X (and after restarting my machine).  It turns out I had to specify the horizontal sync and vertical refresh ranges of my monitor as well.  This information is also in the /var/log/Xorg.0.log file.  For my monitor, I found these lines:

(II) GLINT(0): Supported additional Video Mode:
(II) GLINT(0): clock: 157.5 MHz   Image Size:  356 x 267 mm
(II) GLINT(0): h_active: 1280  h_sync: 1344  h_sync_end 1504 h_blank_end 1728 h_border: 0
(II) GLINT(0): v_active: 1024  v_sync: 1025  v_sync_end 1028 v_blanking: 1072 v_border: 0
(II) GLINT(0): Ranges: V min: 50  V max: 160 Hz, H min: 30  H max: 96 kHz, PixClock max 240 MHz
(II) GLINT(0): Monitor name: NEC FE950+

I took the "Ranges:" line, found more information about the format of the xorg.conf file online, and edited my xorg.conf file further.  Now the "Monitor" section of my xorg.conf file looks like this:

Section "Monitor"
	Identifier	"NEC FE950+"
	Option		"DPMS"
	HorizSync	30-96
	VertRefresh	50-160
	Modeline "800x600"   40.00  800 840 968 1056  600 601 605 628 +hsync +vsync
	Modeline "800x600"   36.00  800 824 896 1024  600 601 603 625 +hsync +vsync
	Modeline "640x480"   31.50  640 656 720 840  480 481 484 500 -hsync -vsync
	Modeline "640x480"   31.50  640 664 704 832  480 489 491 520 -hsync -vsync
	Modeline "640x480"   30.24  640 704 768 864  480 483 486 525 -hsync -vsync
	Modeline "640x480"   25.20  640 656 752 800  480 490 492 525 -hsync -vsync
	Modeline "720x400"   35.50  720 738 846 900  400 421 423 449 -hsync -vsync
	Modeline "720x400"   28.32  720 738 846 900  400 412 414 449 -hsync +vsync
	Modeline "1280x1024"  135.00  1280 1296 1440 1688  1024 1025 1028 1066 +hsync +vsync
	Modeline "1024x768"   78.80  1024 1040 1136 1312  768 769 772 800 +hsync +vsync
	Modeline "1024x768"   75.00  1024 1048 1184 1328  768 771 777 806 -hsync -vsync
	Modeline "1024x768"   65.00  1024 1048 1184 1344  768 771 777 806 -hsync -vsync
	Modeline "1024x768"   44.90  1024 1032 1208 1264  768 768 776 817 interlace +hsync +vsync
	Modeline "832x624"   57.28  832 864 928 1152  624 625 628 667 -hsync -vsync
	Modeline "800x600"   49.50  800 816 896 1056  600 601 604 625 +hsync +vsync
	Modeline "800x600"   50.00  800 856 976 1040  600 637 643 666 +hsync +vsync
	Modeline "1152x864"  108.00  1152 1216 1344 1600  864 865 868 900 +hsync +vsync
	Modeline "640x480"   35.00  640 664 728 816  480 483 487 507 -hsync +vsync
	Modeline "800x600"   56.75  800 848 928 1056  600 603 607 633 -hsync +vsync
	Modeline "1024x768"   94.50  1024 1096 1200 1376  768 771 775 809 -hsync +vsync
	Modeline "1152x864"  104.00  1152 1224 1344 1536  864 867 871 905 -hsync +vsync
	Modeline "1280x960"  148.25  1280 1368 1504 1728  960 963 967 1011 -hsync +vsync
	Modeline "1280x1024"  159.50  1280 1376 1512 1744  1024 1027 1034 1078 -hsync +vsync
	Modeline "1600x1200"  204.75  1600 1720 1888 2176  1200 1203 1207 1255 -hsync +vsync
	Modeline "1792x1344"  220.75  1792 1920 2112 2432  1344 1347 1351 1397 -hsync +vsync
	Modeline "1280x1024"  157.50  1280 1344 1504 1728  1024 1025 1028 1072 +hsync +vsync
EndSection


And voila!  Restarting X - it came up in 1600x1200 without any blue smoke coming out of my monitor, and I could select any of the above resolutions.