A method can include increasing a pressure differential from an interior to an exterior of a packer, thereby deactivating a lock that prevents setting of the packer, and applying a compressive load to a tubular string, thereby setting the packer. A packer can include an annular seal that extends radially outward in response to a compressive load applied to opposite ends of the packer, and a lock that prevents relative longitudinal displacement between sections of the packer, the lock including a radially displaceable piston. In another packer, an inner mandrel can have circumferentially spaced apart engagement structures that are engageable with other circumferentially spaced apart engagement structures, displacement of one packer section relative to another packer section in a longitudinal direction being prevented when the engagement structures are engaged, and such displacement being permitted when the engagement structures are rotationally misaligned.