I only use lighter, subtle overdrive, but I'm also kind of a light OD junkie and have quite a few of them. Here are some suggestions based on what I own and can recommend. This first three are the ones that are currently on my board:
- Spaceman Saturn VI - I love this one as a light, always-on OD and it's currently my favorite lower gain OD. I use it as my always on tone with the Boost at around 1:00, Drive at about 10:00, and the Tone set to taste, usually 11:00 to 1:00. Even with my Stingray and L-2500, the dirt level is fairly mild at those settings but it’s enough to add a pleasing warmth. It will get kind of dirty if you max out the Boost and the Drive, but I never get it into that territory. I'd say this is my favorite so far.
- [sfx] Micro Red Dragon - These have been discontinued for quite a while and don't pop up for sale very often. I got mine for $95 but I was extremely lucky to get it for that price. The last one I saw was $250 and the seller eventually pulled the ad for it. This is one arguably a close second favorite to my Saturn VI and I'm currently using it as a slightly dirtier and slightly darker OD compared to how I have my Saturn VI set. If you can find one, the MRD is worth considering.
- Almost any Blueberry variant that you find and there are many of them, each with their own subtle tweaks to differentiate them. FWIW, I've found all of them I've tried to be very touch sensitive. I have a One Control Blackberry, a Bearfoot FX Blueberry, and a One Control Queen Bee and that's my order of preference, with the Blackberry being the one that's on my board right now. The Body (mids) control on the Blackberry is what makes that one my favorite version so far, but that's probably because of how I'm using it - to get a slightly grindier, slightly dirtier tone than how I have my Saturn VI set. But the Depth control (pre-gain lows) can definitely give you a warmer, thicker tone - and it's interactive with the Gain knob so you have some more flexibility once you see how they interact.
And here are some that I like a lot and, even though they're not on my board, I still can't bring myself to sell them. I might need one as a backup for some of my harder-to-find pedals or I might just want a slightly different flavor of lighter OD to better suit a bass I don't currently gig as often:
- Bearfoot FX Blueberry - I still love my Blueberry and, since they're getting harder to find, I can't see selling it. I find my MRD more versatile overall, but I sometimes think the Blueberry does the darker, warmer OD better than the MRD and consider I swapping those two back and forth to see which wins out overall.
- One Control Queen Bee - Another great Blueberry variant, with a Treble control added to the basic Blueberry circuit. However, I find that the Treble center is kind of high so the Queen Bee doesn't distinguish itself enough from the Blueberry. Not sure I'm going to use it given some of the other light ODs I have, but I can't bring myself to sell it yet.
- One Control Hooker's Green Bass Machine. I like the OD flavor, it doesn't get too dirty, and the Treble knob helps balance between a warmer and darker tone and a having a sharper grit and more articulation. Nice tone and versatile sounding. I do find it Blueberry-like and the Treble control provides a more noticeable control over the tone than the Treble control on the Queen Bee. It's also a mini-sized pedal, so it doesn't take up much room on the board. There's also a newer version out now (the 4K) and I've been tempted to try it, but I have so many light ODs already that I haven't bought one yet.
- EHX Bass Soul Food - This one has generally been despised by most TBers, but I've always liked mine. I suspect that some (many?) who hate it bought it because it's relatively inexpensive without knowing what it's designed for, then blamed it for not being a high enough gain pedal. However, I've noticed that there are a lot more TB'ers who like it these days than there were when it first came out. It does have a Blend knob and it kind of needs it but, with it, it retains the low end well. I'd also suggest keeping the Treble knob below noon to keep it from being too bright and just ignore the Pad switch. It's light enough and subtle enough that you can also use it as a nice clean boost with the gain down low. In fact, even around mid-Gain, you could say it's more of a dirty boost than an overdrive. It's probably the most subtle light OD I own.
- Ampeg Scrambler - I think I'm in the minority but I find it similar to the Bass Soul Food, but with more gain range. FWIW, I strongly prefer its tone with gain below about 2:00 than above 2:00. I think it's too harsh beyond that point. This is one of the few ODs I still have that I might consider selling.
- TC Electronic MojoMojo - Very versatile, I love it on bass with the gain under about noon, but it has more gain than I need so I have it on a small guitar board right now. VERY reasonably priced - $50-ish - and with effective bass and treble controls.
- SolidGoldFX Beta - This is probably the darkest sounding of the light ODs I own. I do like it enough enough to keep it, though. It can get a little buzzy for my tastes at higher gain settings, but below about 2:00 I think it sounds great and I do find it to be pretty touch sensitive. I also find that I like the sound of it even more with the gain and the tone both between about 10:00 and 12:00, which gives a tone that's subtle but warm and full.
I've also seen outstanding reviews of the TC Electronic Spark Booster (full size, not the mini) here on TB, and I see there are several posts in this thread suggesting it. I never tried that one, but I'd like to.
Sorry for the long post, but I do have a good size collection and could give you my opinions on all of them.