Because of the presence of incumbents in cognitive radio networks, the unused spectrum in the TV bands, popularly referred to as ‘white spaces’, are fragmented with the size of each fragment varying from one TV channel to several TV channels. What is more, because the secondary transmissions adjust their spectrum usage over time, white spaces become increasingly partitioned into a collection of discrete fragments, which decreases the spectral utilization. To improve throughputs, most of the prior researches focused on selecting the best transmission channel in the context of spectrum fragmentation but have rarely involved aggregating the fragmentation to a contiguous channel. In this paper, we present two adaptive spectrum access strategies, both of which not only select the best transmission channel but also efficiently solve the fragmentation problem. The first strategy involves one-agile radios that build a transmission using single fragment of frequency, which partially remedy the fragmentation problem using higher-layer solutions. The second strategy suppresses the impact of spectrum fragmentation successfully at the physical layer by combining k spectrum fragments to form a single transmission. The simulation results show that both of the strategies bring larger throughputs compared with the prior solutions. Copyright © 2012 John Wiley & Sons, Ltd.