I own a city bicycle with a very nice 3‑speed Shimano Nexus 3 wheel hub. It is the SG-3C41 model, which has an integrated coaster “backpedal” brake. (The SG-3R40 and SG-3D55 models don’t have that.)
I really dislike coaster brakes, which throw me off balance when maneuvering at low speeds, make starting from a standing position difficult, and generally diminish my feeling of freedom of movement when riding.
Fortunately, it is possible to deactivate the brake. It is an easy modification, and it is completely reversible.
First, download the Inter 3 service manual from the Shimano website. It is a very clear and complete document which shows you around the device, and also has a complete parts list.
Remove the wheel from the bicycle, and extract the hub from the wheel. It is safe to do so; the main roller bearings have their own casings, so no bearing ball is at risk of falling off. There are two metal brake pads inside the hub, held together by a sprung ring. They can be removed by hand.
After removing the pads, you need to tighten down the centrifugally-expanding shaft unit around which the pads sat. The unit must be held together, to prevent it from expanding. A small piece of metal wire will do the job, as shown in the photo below.
If you do not tighten the expanding unit, the hub will work mostly fine; however, you will notice a small lag when engaging after free-wheeling. The lag also pops up when pedaling continuously at low-power, cruising speeds, and is ever so slightly annoying. Tightening the expanding unit makes that disappear entirely.
When reassembling the hub, you will need to tighten two locking nuts on the main shaft. The inner nut is only 3 mm thick, and is turned with a 22 mm key. Just like for any bicycle wheel hub, the two nuts must be tightened against one another at just the right position. Too close to the wheel, and the hub will not rotate nicely around the shaft; too far from the wheel, and the hub will move about slightly, eventually destroying the roller bearings (I learned this the hard way so you don’t have to). Therefore, I highly recommend you use a flat 22-mm key to hold the inner nut, and then tighten the nuts attentively. Flat keys are very inexpensive on Ebay.
Once everything is reassembled, the hub will work as before, except the rider can backpedal freely. There is no noticeable difference.
The Inter 3 hub is a really fine piece of engineering. I must grant that it is not particularly quiet (the lower gears are always freewheeling relative to the upper ones, so it it is only completely silent in first gear). However, the gears are staged just right for urban riding, the service manual is stellar, and, most importantly, the gear switching is flawless. Gears switch instantly, without pedal movement, in a swift and satisfying turn of the wrist. I’ll never go back.