It helps to have a razor with several aggression/closeness settings (e.g. Rockwell 2C or 6S) and switch to milder for across the grain. Or have separate razors for the first and the last pass (like Merkur 34C for start and Henson AL13 for finish).
With a good blade and a very mild razor it might take more passes across the grain but the upside is no nicks and most of the time no bumps.
As always, your mileage may vary because a lot of things influence shaving and it gets pretty individual ¯\_(ツ)_/¯