Forbush decreases (FDs), defined as abrupt and transient reductions in cosmic ray (CR) flux intensity, are fundamental probes for understanding the complex interplay between solar activity and terrestrial weather systems. While previous studies have predominantly focused on events with absolute sizes >3%, small-size events (amplitude ≤3%) and their potential connections to Sun-Earth interactions remain significantly understudied. This research gap arises due to the challenges associated with precise timing and accurate characterization of small-scale events, compounded by the complexities of analyzing other transient astrophysical phenomena. In this study, we employed a state-of-the-art, highly sensitive FD event selection algorithm on daily-averaged CR data spanning 1998–2006 to create catalogs of small-amplitude FDs from nine neutron monitors (NMs) located at low (0–100 m), mid (101–1000 m) and high (>1000 m) altitudes. From the data set, we identified 1956 small-amplitude FDs composed of 766, 601, and 589 events across low, mid, and high-altitude NMs, respectively. Among these FDs, 80, 38, and 19 events were observed to occur simultaneously across the respective altitude ranges. Our analysis shows that the correlation coefficient for small-amplitude FDs and the solar-geomagnetic indices varies appreciably across the three altitude ranges and among the individual NM stations. The same solar/terrestrial variable that indicates a statistically significant correlation with small FDs at some altitude ranges/stations registered marginal or even non-significant relations at other altitudes/stations. These results are indications that small FDs are location-dependent CR phenomena. The results may provide valuable insights into how solar-terrestrial interactions affect CR flux variations across different NM stations and atmospheric levels. This understanding helps improve space weather models and enhances knowledge of CR modulation processes.