Let’s have your overdrive recommendations, then…

tone1

Peacekeeper….I absolutely adore it flat out or dialled right back. 

richman6100

Can't go wrong with a Thorpy Peacekeeper or Nordland ODR-C for crunchy rhythm sounds. I have both and they're very versatile as long as you're not after really high gain. They can do everything from smooth (not what you want) to crisp and 'bitey'. Both work well with a range of guitars and Strat/Tele single coils, P90s, Firebird and humbucker pickups in my experience. I'm currently running two Hamstead Artist amps (which are relatively neutral-sounding) and at relatively low volume, so no amp break-up. Another option might be the Thorpy Warthog. At lower drive settings it has more bite than the other two I've mentioned. Cranked, it does RAT sounds and beyond. If I could only have one drive pedal, I'd choose the Warthog without hesitation.

louis_LLM

Fairfield Barbershop, Greer Tomahawk, Greer Lightspeed, Strymon Deco, JHS Superbolt! 

monquixote

Waza Boss Blues Driver is what I use.

You could also try a Timmy, Nobels ODR, or Bluesbreaker type.

All good and have their own thing going on. 

Kebabkid

I favour early OCDs (V 1.4) but I've also liked the JHS AT & AT+ and the Catalinbread Formula 5f6 - as it is, it's fine and crunches well but there's an internal dip switch which allows for more Marshallesque rather than Tweed sounds

prowla

I've tried a number of Overdrive pedals and TBH I think the first one I had is probably the best - the Boss SD-1.

...up until I decided to check out valve ones...

Right now I like the AMT SS-11B (though it could use a bit of sky blue paint on it).

RandallFlagg

Seymour Duncan 805

Crunchy TS style with 3 band EQ

JJ72

matt_sefton said:

Boss Blues Driver. Cheap, bulletproof, sounds great.

Definitely this for me too....there's a reason it's on a lot of pros boards.
Great rhythm sound that stays true to your clean sound. I've had bluesbreaker styles( prince of tone), klon types and ts types and this has always remained on my board while all others have gone.
Mine is the Keeley version but standard is also great

equalsql

Xotic BB.

Cirrus

Rat, gain low, filter high. Fulfils all your requirements except the 3 band tone control, but... it's a fantastic low gainer.

dilbert

Joyo Sweet Baby, TC Spark and Dano TOD, all do it for me.

stickyfiddle

I’d try a Timmy/JanRay or BB/KoT type or Peacemaker for that brief. 

Maybe also Lightspeed but I didn’t personally like the one I tried

Loobs

I like the Box of Rock, Timmy, OD-3

thomasw88

Barber gain changer
Timmy

Revv g2

Mad prof sweet honey
Trex gristle king

Loobs

Tell you what I didn't like: EQD Plumes...though it seems to sound great for everyone else. 

Fishboy7

I'm constantly changing my gain pedals but have been enjoying the 1981 DRV and Nordvang Gravity at the moment.  

fendermadlewis

Have you tried a modded Blues Driver? Very uncompressed, a lot sweeter after the usual mod kits. If you're handy with a soldering iron you can probably tweak it further to your taste by changing resistor/cap values too  

Neilybob

I'd recommend the 

Ceriatone Horsebreaker Klon/BB but it larger than you specified. I love this pedal. 

Might be worth looking at (though I haven't tried)
TC Electronics Paul Gilbert Mojo. It has a bass and treble knob and it fits the required size and budget. 

JHS PG-13 Paul Gilbert Overdrive

MXR iL Torine Overdrive. 

Or if you are feeling flush with £££ then check out the Wampler Pantheon single. 

andy1839

I'm loving the 1981 DRV and Venuram ODS-1 and Jan Ray, but into Friedman amps.
Since getting a Carr Rambler those haven't worked so well.
The 1981 has a great raspy grind to it, but didn't work so well with the top end in the Carr. 

For the Fender based Carr I've gone with a Suhr Shiba Drive Reloaded Mini and Kingtone Duellist V2 which has a good amount of versatility, although they might be a bit too smooth.

TimmyO

This thread is proof that there is no shortage of very good OD options out there!