Mac Mini does not display HDMI 1080i in full screen on TVs

My identical Mac Mini (1.83Ghz), running Snow Leopard, originally Tiger, has an 1080p option in the display settings. So you should probably upgrade to 10.6, but only if you have 1GB RAM! I bought 10.6 and then had to cram open the mac mini to add RAM to it.

I have been connecting computers to TVs for a long time now.
I have a Mini via HDMI to an older Sony XBR910 HDTV.
Make sure you have "Overscan" in the OSXs "Display Settings" checked.
I an currently using SwitchResX. You only need the "Control Panel".
Open SwitchResX and click your Display on the left.
On the Right select "Custom Resolutions" and then click the "+" on the bottom left.
Use the "Double Arrows" only to resize.
Make it larger or smaller as need. Save it and Restart.
Select the new size in "Display Setting" and see if it's good.
You may have to try a few times until you get it right.
Go back into SwitchResX each time and use the double arrows until you get it right.
You can also click "-" on bottom to remove your previous settings and start over.
Good Luck.
Oh, I also noticed with older Mini's with the Intel GMA950 that sometimes when I start the Mini the display is shifted to the Right. This is easily corrected by selecting a different resolution in Display Settings and when asked to save choose "Revert".
Or switching to another input on my HDMI switch or TV and back also works.

OK, I've read the entire post but am still having problems. I am now using a MacBook Pro, yeah I know not really the right forum section but I searched for other discussions in those areas and did not fine one. Also I will be getting a dedicated Mini soon for this same system - home theater computer. My set up is that the Macbook goes from DVI to HDMI to my Onkyo NR807 which in turn sends video to my 55" LG LCD/LED TV. So I get various "zoom" controls on both the receiver and TV as well as with the Macbook. No matter what combinations of setting I try, including the overscan tip, I either have

1) distorted aspect ratio
2) black borders (got it down to 2 narrow ones, left and right but never totally corrected
3) Cropped image on TV (typically menu bar and dock are cut off)

This is killing me.

For those suggesting or using SwitchResX/DisplayConfigX have you verified both no image distorion (i.e. circles are perfect circles) and that movies play with the proper aspect ratio, i.e. 16:9 or 2:35:1. I'm s stickler for making sure original aspect ratios are preserved.

Hopefully my Mini will be more cooperative but I'd still like to have this working with my MacBook as well.

^ OK, finally got it working. First I removed the receiver from the loop. Then I sent the TV to "just scan" which is the same as 1:1 pixel maping. Finally with mirroring off, and the before mentioned trick of getting 2 1920x 1080 options in the display preferences I get the proper 1080p at exactly 16:9 filling the screen on my LG LCD. Then I added the receiver back in and made sure it was not doing any zooming and it still worked. Would be nice to have this working with and without mirroring.