Similar to the JPEG image compression standard, the JPEG XR image compression solely controls the image quality loss and hence the output rate by means of the quantizer bucket sizes, a precise rate control mechanism like the EBCOT rate allocation algorithm in JPEG 2000 is not specified, and hence rate-distortion optimality of the quantizer is, in general, not given. In this work, a simple rate-control mechanism for JPEG XR is introduced that allows an efficient control of the quantizer towards rate-distortion optimality. One possibility to implement this quantizer control would be to use the spatial variable quantization feature of JPEG XR, but it was seen in an earlier work that the additional side information required to transmit the quantization setting almost compensates the PSNR gain of variable quantization and complicates the rate allocation process by requiring an additional quantizer allocation step. However, while JPEG XR defines the image reconstruction process completely, an encoder still has the freedom to select the dead zone size of the quantizer, this mechanism has the additional advantage that no additional side information needs to be transmitted and that the dead zone size is not, unlike the quantizer bucket size, constrained to a set of pre-defined values specified in the standard. It is found that the image quality of JPEG XR can be improved by about 0.2 to 0.4 dB by performing a rate-distortion optimal selection of the dead zone, this gain is seen to be comparable to the PSNR loss of a JPEG 2000 codec where, for experimental reasons, EBCOT rate control has been turned off.