Neutron rem meters are routinely used for real-time field measurements of neutron dose equivalent where neutron spectra are unknown or poorly characterized. These meters are designed so that their response per unit fluence approximates an appropriate fluence-to-dose conversion function. Typically, a polyethylene moderator assembly surrounds a thermal neutron detector, such as a BF3 counter tube. Internal absorbers may also be used to further fine-tune the detector response to the shape of the desired fluence conversion function. Historical designs suffer from a number of limitations. Accuracy for some designs is poor at intermediate energies (50 keV-250 keV) critical for nuclear power plant dosimetry. The well-known Andersson-Braun design suffers from angular dependence because of its lack of spherical symmetry. Furthermore, all models using a pure polyethylene moderator have no useful high-energy response, which makes them inaccurate around high-energy accelerator facilities. This paper describes two new neutron rem meter designs with improved accuracy over the energy range from thermal to 5 GeV. The Wide Energy Neutron Detection Instrument (WENDI) makes use of both neutron generation and absorption to contour the detector response function. Tungsten or tungsten carbide (WC) powder is added to a polyethylene moderator with the expressed purpose of generating spallation neutrons in tungsten nuclei and thus enhance the high-energy response of the meter beyond 8 MeV. Tungsten's absorption resonance structure below several keV was also found to be useful in contouring the meter's response function. The WENDI rem meters were designed and optimized using the Los Alamos Monte Carlo codes MCNP, MCNPX, and LAHET. A first generation prototype (WENDI-I) was built in 1995 and its testing was completed in 1996. This design placed a BF3 counter in the center of a spherical moderator assembly, whose outer shell consisted of 30% by weight WC in a matrix of polyethylene. A borated silicone rubber (5% boron by weight) absorber covered an inner polyethylene sphere to control the meter's response at intermediate energies. A second generation design (WENDI-II) was finalized and tested in 1999. It further extended the high-energy response beyond 20 MeV, increased sensitivity, and greatly facilitated the manufacturing process. A 3He counter tube is located in the center of a cylindrical polyethylene moderator assembly. Tungsten powder surrounds the counter tube at an inner radius of 4 cm and performs the double duty of neutron generation above 8 MeV and absorption below several keV. WENDI-II is suitable for field use as a portable rem meter in a variety of work place environments, and has been recently commercialized under license by Eberline Instruments, Inc. and Ludlum Measurements, Inc. Sensitivity is about a factor of 12 higher than that of the Hankins Modified Sphere (Eberline NRD meter) in a bare 252Cf field. Additionally, the energy response for WENDI-II closely follows the contour of the Ambient Dose Equivalent per unit fluence function [H'(10)/phi] above 0.1 MeV. Its energy response at 500 MeV is approximately 15 times higher than that of the Hankins and Andersson-Braun meters. Measurements of the energy and directional response of the improved meter are presented and the measured response function is shown to agree closely with the predictions of the Monte Carlo simulations in the range from 0.144 MeV to 19 MeV.