I've been up against higher-offer LOIs in brokered deals, and "won" one after originally "losing" to a higher bidder. I think ^redacted‌'s comments are spot-on.

Digging deep on the structure you're offering vs. the higher overall number may help (e.g., you're at $10M with a 10% seller note; other offer is at $15M with only $5M guaranteed and the remaining $10M on an earnout - whose is better? That's up to seller psychology). What's the seller's day 1 payout? How much if any of the sale price is deferred or at-risk?

Some potential deal-killer points are unlikely to surface at the LOI stages, but could give you a second bite at the apple (e.g., specific structure of non-compete, R&W, indemnity basket and cap, retention plan for key employees, etc.) - generally I think searchers may be more accommodating on these points than a PE firm or strategic buyer.

And especially in "smaller" small businesses, fit / legacy / cultural integration can't be ignored. It probably won't get you a multimillion-dollar discount, but it's one of the factors that's typically most strongly in your favor.

I think it's key that you don't burn a bridge. I often get a "higher offer" but from a riskier buyer. Sellers will typically want to chase the higher offer even knowing that it may not close. I'm always hopeful that the better buyers aren't offended that the seller chases the money a little bit to see where it goes.