Modules for converting at least a portion of an existing stairway into an alternating stairway are described. The modules may be installed over an existing stairway to improve accessibility of the stairway for the very young, elderly, ill, injured, or disabled. Installation of the modules creates an alternating stairway presenting a step height that is about one-half the step height of the existing stairway, without appreciably changing the horizontal run or height of the stairway.