Firm wants to know compensation details of an offer I've received help

I've applied to a few different firms and received a single offer so far that is relatively competitive but I already know the 1st year compensation package for the firm inquiring about the compensation details is higher than the offer I received.

I also know that they're willing to negotiate a bit higher and have some wiggle room and I don't want to give up any advantage on my end by revealing the offer I currently have is probably below their initial offer from what I've heard. How can I word this so that I don't have to reveal the compensation of the offer I received (from a competitor, so it's not an irrelevant firm in terms of compensation) and still push for an increase over the typical 1st-year compensation package for the firm inquiring?

The skillset I currently have is very high in demand and I know market level for this position is higher, is there a way to negotiate or subtly ask for an increase in total comp by relying on market data, knowledge/experience, and the fact that they'd be taking me away from one of their main competitors?