Dispersive mirrors based on time-domain approach are compared with mirrors resulting from conventional phase target designs. Phase targets have been applied to complementary-pair dispersive mirrors, used for sub-5-fs pulse compression. While the phase approach has hither to afforded the best performance for the shortest pulses, our new approach, based on time-domain targets and tailored for a specific input spectrum, appears to provide comparable performance for pulse compression for a pulse duration 4.6 fs. Experimental studies using dispersive mirrors made to both designs are described.