Artificial PbTiO3/SrTiO3 superlattices were constructed using off-axis rf magnetron sputtering. X-ray diffraction and piezoelectric atomic force microscopy were used to study the evolution of the ferroelectric polarization as the ratio of PbTiO3 to SrTiO3 was changed. For PbTiO3 layer thicknesses larger than the 3-unit cell SrTiO3 thickness used in the structure, the polarization is found to be reduced as the thickness is decreased. This observation confirms the primary role of the depolarization field in the polarization reduction in thin films. For the samples with ratios of PbTiO3 to SrTiO3 of less than one, a surprising recovery of ferroelectricity that cannot be explained by electrostatic considerations was observed.