Health issues for elderly people may lead to different injuries obtained during simple activities of daily living. Potentially the most dangerous are unintentional falls that may be critical or even lethal to some patients due to the heavy injury risk. In the project "Wireless Sensor Systems in Telecare Application for Elderly People", we have developed a robust fall detection algorithm for a wearable wireless sensor. To optimise the algorithm for hardware performance and test it in field, we have designed an accelerometer based wireless fall detector. Our main considerations were: a) functionality - so that the algorithm can be applied to the chosen hardware, and b) power efficiency - so that it can run for a very long time. We have picked and tested the parts, built a prototype, optimised the firmware for lowest consumption, tested the performance and measured the consumption parameters. In this paper, we discuss our design choices and present the results of our work.