MSR WhisperLite backpacking stoves are ubiquitous, but they lack a key function: the ability to simmer easily. How can you set a WhisperLite to simmer without having to constantly watch the stove and micro-adjust the fuel valve?
The short answer: don't. Edit: Instead of simmering on the stove, remove the pot from the flame and keep it insulated to retain heat. See @KateGregory's excellent answer for more details.
The long answer: you can reduce the pressure in the fuel bottle, and this will reduce the flow rate of the fuel.
This is done by pumping fewer times! The exact number will vary over bottle size and amount of air in it--how full it is.
After you brought your pot to a boil, using the stove at regular pressure as per the manual, remove the pot from the stove and turn off the gas valve. Once the stove is off, take a hold of the bottle, hold it up vertically, and carefully unscrew the pump to release the pressure. Do this carefully, and be sure there is no flame immediately nearby, because if the fuel vapour lights up, you are going to have a very bad time. Once the pressure is released, re-seal the pump on the bottle, give it one or two pumps, open the fuel valve and relight the stove. If your flame is still too strong, repeat this procedure with fewer pumps. Ultimately, it's the pressure in the fuel bottle that determines the flow to the stove.
The vapour coming out as you depressurize the fuel bottle can catch fire if you are not careful. You must be sure there are no fire sources nearby that will light it!
Given the risk involved, I think it's best to avoid doing this. I have been able to make fancy rice, soup, sauce, eggs, pancakes, and other types of meals that benefit from simmering on this stove with regular operation. An easy solution is to simply elevate the pot higher over the fire. If you know you will be in a setting that calls for long-term simmering, then an LPG stove will do a much better job of it.
When I get to the "simmer" part of cooking on the Whisperlite, I take the pot off the stove, put the lid on, and wrap it in a towel including underneath and on top. Whatever I am cooking will stay simmery for at least 20-30 minutes that way. It's great for making a sauce with dehydrated ingredients. While the sauce is sitting aside staying hot, I can cook pasta or rice with the stove. It's one of the tricks to eating well in the backcountry without taking a lot of equipment. Pasta with sauce over it, or rice with sauce over it, tastes better than a one-pot all-mixed-up meal. And if you have kids with you, you can accomodate their desires for more sauce, less sauce, or the sauce not to touch the starch. Everybody wins.
As an alternate solution, if you are doing a lot of simmering and don't mind taking an additional piece of equipment, look into heat diffusers. There is even a company that makes back-country ovens based on the principle of heat diffusion and insulation. All these ovens are is a heat diffuser, a pan with a lid and a thermometer, and a cozy for the pan.
While the depressurization trick does work very well, its also not necessary. I've used the whisperlite to simmer just by turning the flame down real low. You have to be very gentle on the valve and be looking right at the flame to gauge it, but it works.
Based on experience using this stove for 70+ days of trail work (breakfast and dinner each day).
After reviewing many blogs on this topic and running some experiments, I think I found something else helpful. I have an old Whisperlite from around 1999 or 2000. When Coleman gas could not be controlled, I cleaned it out thoroughly and switched to MSR Super Fuel. The Super Fuel is wonderful and I am able to control a steady simmer without problems on a clean stove. I also applied the low pressure technique (from the start) and works great.
If you have extra fuel, extra water, and a spare frypan you can also use the double-pan technique.
Put the water in the frypan and then your pot in the water. The water in the frypan will buffer the temperature of the stove a bit more and if you turn off the stove it’ll buffer the cooling as well.
It’s hugely wasteful of gas and water though.