The little giant is a 5/3w (single-ended) SE amp. I'd tried it on at 5w, and I gotta say the clean headroom is amazing. Thing is, the amp really shines only when the power amp tubes are saturated; that's when you get that 'tube' sound. Not so much of preamp distortion/overdrive.
When you use pedals to drive, that's pretty much gonna get you a preamp distortion/overdrive. To get that nice saturation, you gotta crank it up.
So the ultimate solution for you, I'd reckon will be to use an attenuator. Although, you gotta understand that when you run your tubes hot, *which you will, with an attenuator*; the tube life will be shortened significantly.
Power tubes are not cheap to replace; but you can rejoice as SE amps don't need rebiasing! I never knew this as when I was still in Singapore, I played through mostly preamp, and never really cranked up the amps enough to get that 'tube gain'.
with 3watts, you may be able to crank it up without blowing up walls.... but then again, the clean headroom will be compromised (it will break up earlier).
all in all, my 2cents is that you should get an attenuator (THD, powerbrake, or other varieties out there). This might just help you with volume levels, BUT you will be missing out on other factors such as having the speaker/cabinet characters being brought out; and you will be having shorter tube lifespan.
if you're more than happy with 3watts, get an overdrive pedal (decent one), and then pump up the volume to that of an acceptable level and rock on!
The THD is a more viable option IMO if you need the headroom; just remember to save up and set aside cash to service the power tube when you need to!
Cheers