Starlight corrupted by atmospheric turbulence cannot couple efficiently into astronomical instruments based on integrated optics as they require light of high spatial coherence to couple into their single-mode waveguides. Low-order adaptive optics in combination with photonic lanterns offer a practical approach to achieve efficient coupling into multiplexed astrophotonic devices. We investigate, aided by simulations and an experimental testbed, the trade-off between the degrees of freedom of the adaptive optics system and those of the input waveguide of an integrated optic component leading to a cost-effective hybrid system that achieves a signal-to-noise ratio higher than a standalone device fed by a single-mode fiber.