Negotiated a Jane Street offer earlier this year. Here's what worked and what didn't, since most negotiation advice is written for RSU-heavy FAANG offers and doesn't map cleanly to the JS comp structure.
What I tried to negotiate: Base salary Signing bonus 'Target' bonus expectation
What moved:
Base: moved about $15k after I came back with a specific competing offer. The key was having a real number, not a vague reference. I said 'I have a written offer at $X from Y company at comparable level' and they came back within 48 hours with an updated number. They're not going to dramatically close a gap but they will close a reasonable one.
Signing: this was actually easier to negotiate than I expected. They added $50k signing when I pushed, partly because it doesn't affect their recurring cost base. Standard signing cliff was 12 months (repay if you leave before then). I pushed for 6 months and they split the difference at 9. Doesn't always work but worth asking.
Bonus target: they won't formally change the 'target' percentage. That's set by level and is firm-wide. What they told me is that the starting level calibration matters a lot more than the target percentage, and if you feel you're being leveled below your actual scope that's a better argument to make.
What didn't move: the discretionary nature of the bonus. I asked if there was a minimum floor or guaranteed floor and they were clear: no. Discretionary means discretionary. They were not defensive about it, just matter-of-fact.
Timing: they gave me 5 business days to decide on the verbal offer. I asked for 10 and got 7. Felt reasonable.
General read: they're more flexible than their reputation suggests but the leverage is having a real competing number. 'I'm weighing other options' without specifics does nothing.