We have calculated finite-size correlation lengths for strips of the square-lattice Ising spin glass using the transfer-matrix method. In order to minimize sampling errors we study strip lengths up to 5×106 lattice spacings. A phenomenological renormalization-group analysis indicates that there are strong corrections to simple power-law scaling near the zero-temperature critical point, as is to be expected near a lower critical dimension. We examine models with Gaussian, exp(-J2/2), and exponential, exp(-‖J‖), distributions of couplings; the Gaussian distribution shows stronger finite-size corrections. The correlation-length exponent is estimated to be ν=4.2±0.5, although we do not want to rule out the possibility that ν is significantly larger than this.