Embodiments of the invention provide apparatus and methods for insulating a structure. A method for insulating a structure may include providing a frame that comprises a plurality of frame members coupled together. Sheathing panels may be coupled to the frame members such that adjacent sheathing panels abut and directly contact each other at an interface to form a wall having a front surface and a rear surface. A spray insulation material may be applied to the front surface of the wall such that the insulation material forms a substantially continuous insulation layer atop the front surface and such that the insulation material directly contacts the interface between adjacent sheathing panels to restrict passage of air between the adjacent panels to at or below 0.2 L/m2/s at a differential pressure across the wall of 75 Pa. The insulation layer may provide an R value of at least 5, or in some embodiments at least 10.