Abstract There are several peculiar long-period dwarf-nova-like objects that show rare, low-amplitude outbursts with highly ionized emission lines; 1SWASP J162117+441254, BD Pav, and V364 Lib are among them. Some researchers even doubt whether 1SWASP J1621 and V364 Lib have the same nature as normal dwarf novae. We studied the peculiar outbursts in these three objects via our optical photometry and spectroscopy, and performed numerical modeling of their orbital variations to investigate their properties. We found that their outbursts lasted for a long interval (a few tens of days), and that slow rises in brightness were commonly observed during the early stage of their outbursts. Our analyses and numerical modeling suggest that 1SWASP J1621 has a very high inclination, close to 90°, plus a faint hot spot. Although BD Pav seems to have a slightly lower inclination (∼75°), the other properties are similar to those in 1SWASP J1621. On the other hand, V364 Lib appears to have a massive white dwarf, a hot companion star, and a low inclination (∼35°). In addition, these three objects possibly have a low transfer rate and/or large disks originating from the long orbital periods. We found that these properties of the three objects can explain their infrequent and low-amplitude outbursts within the context of the disk instability model in normal dwarf novae without a strong magnetic field. In addition, we suggest that the highly ionized emission lines in outburst are observed due to a high inclination and/or a massive white dwarf. More instances of this class of object may be unrecognized, since their unremarkable outbursts can be easily overlooked.