Assuming you have a PSC blower motor
If you go to the blower motor , there are 3 wires connected at the blower, namely red,blue,black,white..The white is always neutral. Now when power goes to red, it is the lowest speed, to blue it is medium speed and to black it is the highest speed.Normally the incoming power black is wired to black on the motor so that when you call for fan "on" the black is energized giving you the highest speed.
To reduce the speed, disconnect the black to black tie and then tie the red to incoming black.

Of course if you do that, there is a good chance without confirming that the AC speed which shares the fan on speed may be too low, causing frozen coil, slugging refrigerant and evential compressor failure. If you do this shut off outdoor AC so you remember to switch it back before cooling season.

Not familiar with that Rheem unit and just adding that if it had been variable speed the fan speed option would have been built in, check to see if you have a constant fan terminal which on some boards is in addition to the cool and heat speeds which offers a third selection for constant fan.

I once years before this option was thought of achieved this third speed activated by fan switch and kicked up to cooling speed when ac called by adding a couple relays in blower compartment. It can be done for less than $25.

Thanks for the input everybody. I found out that whichever lead is connected to the "heat" plug is the one that is used in "fan" mode. A friend has my laser thermometer, so until I get it back I won't be switching the "low" fan speed to the "heat" plug. Once I get the thermometer back I'll switch them, then run the heat and measure the output temp to see if it's within the range specified in the manual.

Does that sound right? As I said before it's rare that we even use the furnace, and we could probably get by without using it at all since we have a gas insert fireplace with a blower and there is a return air duct near the fireplace so we can use the fireplace with the air handler fan on during real cold nights (28-30F in Houston)and that will probably keep the whole house above 65F (our winter stat setting). I should have added the house was built in '08 and it's energy start certified, so it's pretty tight.

I really wish we had a variable speed system but it would be a waste to replace a brand new 14 seer r-410 system (even though it is builders grade).

Hmmmm, I thought Rheem ran the fan on at the heat speed, not the cool speed.

baldloonie- You are correct, it does run it at the heat speed. I must not have explained what I found in my Jan 4th post very well.

I tried to say that I had found that whatever lead (from the fan motor) is connected to the heat plug on the board is the speed that will be run in fan mode. I also mentioned that I wasn't going to connect the low speed wire to the heat plug until I could test the furnace output temp in low speed to make sure it wouldn't be too hot and out of the range specified in the manual.

Another option, if energy savings is the goal, is to get a programmeable thermostat that allows you to independently control the fan mode for each period. My thermostat has, "auto", "on" and "circ", which runs the fan 33% of the time regardless of demand. I can then control which fan mode is active during each peroid. My winter program has the fan "on" for 2 hr, "circ" for 6 hrs, and "auto" for 16 hrs a day, depending on when I'm home and what I'm likely to be doing.

I never thought of that. My tstat has a "circ" setting as well, but I never even gave it a thought that I could program the different fan settings for different times.

Thanks for the suggestion chris8796.

I have the opposite problem. I just had a Reeme AC installed. When I put it on fan "ON". temp to off. the fan only runs in low mode. You can not even tell its running. The AC company said this is because its a variable speed motor. I think they are wrong.

hello Michael, Did you find any solution for tgis problem ?