A mobile wireless device adapts transmit power levels and number of retransmissions of a preamble sent to a wireless network. The mobile wireless device measures characteristics of a downlink signal received from the wireless network. The mobile wireless device transmits a series of preambles to the wireless network, each successive preamble having an increased power level, starting at a power level based on the measured received signal characteristics and on parameters received from the wireless network, up to a maximum transmit power level. When the transmit power level of the preamble exceeds the maximum transmit power level and when the measured downlink signal quality falls below a threshold, the mobile wireless device limits the number of preamble retransmission to less than an allowed maximum number of retransmissions. A minimum number of retransmissions is determined and adapted to higher values for larger measured values of downlink signal quality.