Recently, a light sheet-based technique called objective-coupled planar illumination (OCPI) microscopy [Holekamp et al., Neuron 57, 661 (2008)] was shown to permit low-phototoxicity, high-speed, three-dimensional fluorescence imaging of extended tissue samples. Here, we introduce two major improvements in OCPI microscopy. First, we miniaturize the objective coupler by using a uniaxial gradient-index lens to produce the light sheet. Second, we demonstrate theoretically and experimentally that refractive index mismatch at the fluid/tissue interface causes a significant defocus aberration. By introducing the ability to tune the angle of the light sheet, we show that defocus correction in a miniaturized OCPI microscope leads to a significant improvement in image sharpness deeper into tissue.