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To improve beam penetration into a head allowing the treatment of deeper seated tumors, two neutron collimators were built sequentially and tested for use in the clinical boron neutron capture therapy (BNCT) program at the epithermal neutron irradiation facility of the Brookhaven Medical Research Reactor. The collimators were constructed from lithium-impregnated polyethylene, which comprises Li2CO3 powder (approximately 93% enriched isotopic 6Li) uniformly dispersed in polyethylene to a total 6Li content of 7.0 wt. %. The first collimator is 7.6 cm thick with a conical cavity 16 cm in diameter on the reactor core side tapering to 8 cm facing the patient's head. The second collimator is 15.2 cm thick with a conical cavity 20 cm in diameter tapering to 12 cm. A clinical trial of BNCT for patients with malignant brain tumors is underway using the first collimator. Results of phantom dosimetry and Monte Carlo computations indicate that the new 15.2 cm thick collimator will improve the neutron beam penetration. Thus, the second collimator was made and will be used in an upcoming clinical trial. In-air and in-phantom mixed-field dosimetric measurements were compared to Monte Carlo computations for both collimators. The deeper penetration is achieved but at a sacrifice in beam intensity. In this report, a performance comparison of both collimators regarding various fluence rate and absorbed dose distributions in a head model is presented and discussed.