Moderately deep near-infrared images are used to investigate the photometric properties and spatial distribution of bright giants near the centers of the core-collapsed globular clusters NGC5946 and NGC7099. The former cluster is located at a low Galactic latitude and is heavily reddened; nevertheless, the K, J-K color-magnitude diagram (CMD) shows a well-defined giant branch, with a width +/- 0.05 magnitudes in J-K. Most of the observed width is due to differential reddening. The upper giant branch is relatively steep, and comparisons with less reddened clusters indicate that (1) NGC5946 must be very metal-poor, with [Fe/H] ~ -2, and (2) E(B-V) ~ 0.6. The distance to NGC5946 derived using the near-infrared brightness of the giant branch tip is in excellent agreement with that computed from the V brightness of the HB if E(B-V) = 0.6. The NGC7099 giant branch terminates ~ 1 mag fainter in K than the expected tip brightness. The integrated J-K color of NGC7099 changes with radius, such that Delta (J-K) /Delta log(r) = 0.05 - 0.09, depending on the technique used to measure colors. Similar radial variations in stellar content might be expected in NGC5946; however, the integrated J-K color of this cluster remains constant with radius and, after removing the brightest resolved stars, a color gradient is seen that is in the opposite sense to that in NGC7099. The relative density of bright giant branch stars also remains constant within 30 arcsec of the center of NGC5946. Therefore, it is concluded that NGC5946 does not contain stellar content gradients similar to those seen in NGC7099 and other post core-collapsed clusters.