Bound states in the continuum (BICs), as a rule, are studied in spatially regular or symmetric structures that provide a clear interpretation of the interference underlying the BIC formation mechanism and its practical realization. On the other hand, irregular asymmetric structures with poorly interpreted ‘accidental’ BICs are typically left out of the scope due to the excessive abundance of parameters. In the present paper, we theoretically address spatially irregular structures and generalize the recently proposed concept of Fourier-BICs [Phys. Rev. Lett. 136, 156904 (2026)] to that extent. We consider the waveguide-based Fabry-Perot (FP) resonator with N mirrors (resonators) located irregularly and derive an explicit BIC formation condition in the limit of weak scattering of the propagating wave by the mirrors. It requires the vanishing of an N-term exponential sum, representing a ‘Fourier transform’ of the bound states in the evanescent mode calculated at irregular points of the resonators’ positions. It turns out that in the case of weakly scattering identical mirrors, only regular or symmetric structures possess Fourier-BICs for N < 5. Whereas, for N ≥ 5, Fourier-BICs in a waveguide with all distances between adjacent resonators being different become possible. When the mirrors are not infinitesimal, these BICs continuously transform and demonstrate much more complex behavior including the possibility of BICs with irregular inter-mirror distances for smaller N. Analytical considerations are supported by examples of numerical calculations of two-dimensional quantum-mechanical and optical waveguides. The revealed BIC formation condition offers a regular way for designing irregular systems possessing BICs, suggesting, for instance, a universal approach to the design of waveguide systems providing BIC-assisted decoherence suppression.