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We show that very compact axion mini-clusters can form in models where axion-like-particle (ALP) dark matter is produced via the kinetic misalignment mechanism, which is well-motivated in pre-inflationary $U(1)$ symmetry breaking scenarios. This is due to ALP fragmentation. We predict denser halos than what has been obtained so far in the literature from standard misalignment in post-inflationary $U(1)$ breaking scenarios or from large misalignment. The main reason is that adiabatic fluctuations are significant at early times; therefore, even if amplification from parametric resonance effects is moderate, the final size of ALP fluctuations is larger in kinetic misalignment. We compare halo mass functions and halo spectra obtained in kinetic misalignment, large misalignment, and standard misalignment, respectively. Our analysis does not depend on the specific model realization of the kinetic misalignment mechanism. We present our results generally as a function of the ALP mass and the ALP decay constant only. We show that a sizable region of this ALP parameter space can be tested by future experiments that probe small-scale structures.