DECT (Digitally Enhanced Cordless Technology) phones use a digital signal that is both powerful and clear.  These transmit and receive their radio signals in the 2.4 Ghz (2450 Mhz) just like Wi-Fi devices, newer video baby monitors and microwave
ovens! Studies show cordless phone use to be as conducive to cancer risk as the use of cellphones. 
When not in use, a 2.4 Ghz DECT base station emits pulses at 100 hertz as a location beacon for its handset. A study of 25 subjects found that 40% of them
experienced varying degrees of sensitivity to the 100 hertz digital pulse from the 2.4 Ghz
base station. Only 3% of the population has a severe reaction while most others are only moderately to slightly affected. They experienced tachycardia or racing or pounding of the heart whenever that signal was turned on three feet from their supine bodies.  The other 60% of subjects were found to be non-responsive to the 'Agent' but one precaution is not to sleep with a cordless station next to your bed but replace it with a corded handset.
Both DECT Cordless phones and Wi-Fi devices have become available in the 5.8
GHz band. It seems counterintuitive but while DECT cordless phones are not being used, that is, "on standby" or "receive-only" as they await a call or their owner to pick up and make a call, the base stations of most models continuously emit microwave radiation at full power as long as the base station is plugged into an electrical outlet. The base unit radiates 24/7 whether the phone is being used or not.
Using Bluetooth headsets to talk wirelessly to your cell phone may be worse than holding the phone to your ear: The headsets are so new there are no studies on them yet. Mercola has tested Bluetooth headsets measuring over 100 milligauss while in use. Acceptable range should be 3 or less.  Many of these headsets are inserted deeply in your ear canal so their radiation is closer inside your head than using the phone itself. A "non-Bluetooth headset is preferred but even here you need to be cautious. While hands-free devices have been found to reduce radiation from cell phones, emissions can still travel up the headset wire and into your head." Risk of acoustic neuromas doubles over the course of a decade of cordless phone use.
Keep cordless phone bases out of the bedroom; their close proximity, especially while your body is trying to rebuild itself during the sleep, is especially harmful.  If you just cannot go back to using a corded phone then one of the low radiation DECT cordless models is an alternative. These reduce their RF output depending on distance and turn off their transmissions when you're not using them ... just as you would expect. Regular models continue to transmit so they will be ready with a channel open when you turn them on to use. One such model is made by Gigaset but it's not cheap.