Embodiments include methods performed by a wireless device for random access to a wireless communications network. Such methods include transmitting a random access preamble in a first uplink (UL) bandwidth part (BWP) of a carrier and selecting a first downlink (DL) BWP of the carrier based on an association between the first UL BWP and the first DL BWP. Such methods include monitoring the first DL BWP for a random access response from the wireless communication network to the transmitted random access preamble. Other embodiments include complementary methods for a base station configured to support random access by wireless devices, as well as wireless devices and base stations configured to perform such methods.