Our previous studies on low-frequency electromagnetic cyclotron waves (ECWs) with amplitudes larger than 0.1 nT in the solar wind revealed that the left-handed (LH) polarized ECWs are the dominant waves, and these waves preferentially occur in plasma conditions of high proton speed (Vp), high proton temperature (Tp), low proton density (Np). In the present study, using magnetic field and plasma data from the Wind mission between 2005 and 2015, we perform a survey of small-amplitude ECWs with amplitudes smaller than 0.1 nT. It is revealed for the first time that the small-amplitude right-handed (RH) polarized ECWs tend to frequently occur in plasmas characterized by low Vp, low Tp, low Np, although the small-amplitude LH ECWs still preferentially occur in plasma conditions similar to the LH ECWs with amplitudes larger than 0.1 nT. Further investigation shows that the occurrences of small-amplitude RH ECWs and long-lasting radial interplanetary magnetic field (lrIMF) share the similar preferential plasma conditions of low Tp and low Np. During lrIMF events, in particular, the occurrence rates of RH and LH ECWs are comparable, with the occurrence rate of small-amplitude RH ECWs slightly larger than that of small-amplitude LH ECWs. The generation mechanism of the small-amplitude ECWs is discussed.