ABSTRACT Monitoring wildlife population trends often involves indices assumed to correlate in proportion to abundance. We used aerial count data and harvest statistics for moose ( Alces alces ) populations in 16 hunting districts of Montana, USA, spanning 32 years (1983–2014) to assess population trends, drivers of uncertainty about those trends, and the relationship between aerial counts and hunter catch‐per‐unit‐effort (CPUE). We found a great deal of statistical uncertainty surrounding population trends of moose measured with aerial minimum‐count data, despite time series averaging >15 annual counts/district. State‐space models of count‐based trends suggested declining populations in 11 of 16 districts, yet 95% credible intervals overlapped 0 in all cases. The precision of count‐based trends improved with increases in the number of years spanned by the time series (β = −0.003, P < 0.001) and average number of moose counted per survey (β = −0.0006, P = 0.002). Calibration of CPUE with count data showed positive correlations in only 5 of 16 (31%) districts and a catchability exponent (β) significantly <1. This indicated a generally poor level of agreement between these 2 indices, and evidence of “hyperstability,” wherein declines measured by aerial counts were not reflected by proportionate declines in CPUE. Additionally, long‐term trends measured with CPUE were not correlated to those in aerial counts ( P  = 0.61). We encourage explicit attention to the precision of trend estimates and local calibration of population indices to ensure both positive and proportionate relationships to underlying patterns of abundance. © 2016 The Wildlife Society.