In this work, a novel strategy for lowering the uplink user exposure index (EI) is described for an indoor narrowband use-case. This metric measures the long term exposure to electromagnetic radiation a user receives from a device operating in the uplink from the user terminal to the access point. The specific type of device chosen for the exposition of this novel method was a laptop computer and results presented herein specifically target an aspect of this metric called the specific absorption rate (SAR). It is firstly shown that SAR, in the context of a laptop, may be modeled in a similar fashion to the more familiar smartphone analyses that appear in literature. Secondly, an algorithm comprising a mixture of precoding and power control is proposed for usage in the uplink where it is seen to reduce uplink user EI. This proposed approach can provide a reduction in the long-term exposure of the user or be used as a means to increase the transmit power of the device while maintaining SAR compliance. It is shown that if quality-of-service (QoS) is maintained, the proposed approach can achieve a median reduction in SAR of 50 %, which in turn is seen to lower the EI by 30 %. Furthermore, a 60 % median reduction in SAR may also be possible if a minor degree of decrease in QoS is tolerated, which in turn is seen to lead to a 50 % reduction in the EI.