Recent standardization of portions of the millimeter-wave (mm-wave) band for fifthgeneration (5G) operation has called for further research on how short-term fading behaves in that unexplored part of the spectrum. With such a target, this paper reports on a thorough measurement campaign conducted in an indoor environment characterized by rich-multipath scattering, a part of a modern building, with floor and ceiling constructed of reinforced concrete over steel plates with wood and plasterboardpaneled walls. Particularly, measurements have been performed in a variety of scenarios, under line-ofsight (LoS) and non-line-of-sight (nLoS) conditions, for a wide range of frequencies, namely from 25 to 40 GHz -a span of 15 GHz -therefore, including 26, 28 and 39 GHz. First and second order statistics of representative fading models, namely Rayleigh, Rice, Nakagami, folded normal, α-µ, η-µ, κ-µ, and α-η-κ-µ have been investigated. The metrics used in the analysis were the normalized mean square error (NMSE), the Kolmogorov-Smirnov (KS), and the Akaike information criterion (AIC). Additionally, the study of the κ-µ model is advanced, in which new, exact, simple closed-form expressions for probability density function, cumulative distribution function, and level crossing rate are derived for some particular cases, namely for µ = n + 1/2 in which n ∈ N.