How can I get rid of a 4khz-8khz room spike?

Thanks for the replies and comments. I think my approach will be to install some 4khz+ traps on the walls and see if this makes any difference. Maybe remove and/or reposition some room tunes as Edle suggests. If no significant effect, I will then look at power supply per comments of Cincy bob.

Herman: how do I properly set up a nearfield measurement?

Cincy bob: please advise how you compensate for RS SPL meter inaccuracies.

Onhwy61: I measured using the meter mounted on a tripod positioned at my head location on my listening chair and on the tripod in the same location with the chair removed from the room. No noticable change in response. Measurements were taken using 10s weighted average readings (C-weighted). I repositioned speakers two more times by up to 18" each with only a slight reduction in the magnitude of the spikes. Used both Paradigm S60V3 and Triangle Antal XS speakers - results were relatively the same with the hotter Antals having higher peaks within the same general range.

Thanks.

Nanotweeter, if you launch the link in Herman's post above, you will see a 2001 thread that was initiated by Sean and that includes a compensation chart of adjustments that need to be made at each 1/3 octave interval in order to adjust for the inaccuracies of the Shack meter. Those compensation adjustments are summarized below:

10Hz.....+20.5
12.5Hz...+16.5
16Hz.....+11.5
20Hz.....+7.5
25Hz.....+5
31.5Hz...+3
40Hz.....+2.5
50Hz.....+1.5
63Hz.....+1.5
80Hz.....+1.5
100Hz....+2
125Hz....+0.5
160Hz....-0.5
200Hz....-0.5
250Hz....+0.5
315Hz....-0.5
400Hz....0
500Hz....-0.5
630Hz....0
800Hz....0
1kHz.....0
1.25kHz..0
1.6kHz...-0.5
2kHz.....-1.5
2.5kHz...-1.5
3.15kHz..-1.5
4kHz.....-2
5kHz.....-2
6.3kHz...-2
8kHz.....-2
10kHz....-1
12.5kHz..+0.5
16kHz....0
20kHz....+1

Add the above numbers to your SPL meter readings in order to obtain the actual SPL level in your room at each 1/3 octave interval. Given the -2dB compensating adjustments required at your problematic treble frequencies, I think you will find that you still have a reduced but still very sizable 8dB or so frequency response spike throughout those frequency bands.

Nanotweeter...If you must use the RS meter, use it with the Rives Audio CD that has tracks which are corrected for the RS meter error.

My personal experience is that a spectrum analyser (such as the Behringer DEQ2496) is a thousand times better.

I have a similar room - 13' x 15' and highly reflective. Nasty 8 dB peak in same area you have. At one point I had the room entirely covered with carpets and blankets and such and still the same peak. Didn't matter which speakers I used until.....
I have now solved the problem by changing speakers - and no acoustic treatment. I went to a single driver speaker which beams over 3kHz so no room reflections. Works GREAT in a small room such as yours. It's like listening to headphone but with great soundstaging.
Some good full range drivers:
Jordan JX92s (~$310/pr)
Adire WR-125 or FR-125 from www.creativesound.ca ($150/pr)
Tang-Band W4-1320 available July from www.partsexpress.com ($75/pr.)
Other brands: PHY, AER, and Fostex FR-120 or FR-200.