The dust complex G159.6-18.5 in the Perseus region has previously been observed with the COSMOSOMAS experiment on angular scales of ~1°, and was found to exhibit anomalous microwave emission. We present the first high angular resolution observations of this dust complex, performed with the Very Small Array (VSA) at 33GHz, to help increase the understanding of the nature of this anomalous emission. On the angular scales observed with the VSA (~10-40arcmin), G159.6-18.5 consists of five distinct components, all of which are found to exhibit an excess of emission at 33GHz that is highly correlated with far-infrared emission. Within the region, we find a range of physical conditions: one of the features, which is associated with the reflection nebula IC 348, has a dust emissivity comparable to that of HII regions, while the other four features have values in agreement with previous observations of intermediate Galactic latitudes. We provide evidence that all of these compact components have anomalous emission that is consistent with electric dipole emission from very small, rapidly rotating dust grains. We find that these five components contribute ~10 per cent to the flux density of the diffuse extended emission detected by COSMOSOMAS, implying that the bulk of the anomalous emission in Perseus is diffuse and not concentrated in these compact components.