Aims. Narrow-angle tailed (NAT) sources in clusters of galaxies can show on the large scale very narrow tails that are unresolved even at arcsecond resolution. These sources could therefore be classified as one-sided jets. The aim of this paper is to gain new insight into the structure of these sources, and establish whether they are genuine one-sided objects, or if they are two-sided sources. Methods. We observed a sample of apparently one-sided NAT sources at subarcsecond resolution to obtain detailed information on their structure in the nuclear regions of radio galaxies. Results. Most radio galaxies are found to show two-sided jets with sharp bends, and therefore the sources are similar to the more classical NATs, which are affected by strong projection effects.