Channel access procedures of the state-of-the-art cellular standards create a significant overhead for small messages transmitted by Internet of Things (IoT) devices. As IoT becomes a major source of traffic for next-generation wireless communications, there are recent efforts to design low-overhead access schemes. Here we present the delay and capacity analysis of two low-overhead access protocols in a setting similar to LTEM which is recently standardized for IoT communications. The first protocol that we evaluate is an ALOHA-like immediate transmission scheme where the data is transmitted without channel reservation. The second protocol is a preamble-initiated contention-based access scheme where a frequency/time resource is imperfectly reserved by the transmission of a random preamble. Our results show that preamble-initiated contention-based access improves small message throughput 86% both with respect to the ALOHA-like scheme and the conventional LTE channel access. On the other hand, the ALOHA-like scheme provides 62% lower delay in comparison to the preamble-initiated contention-based scheme at low traffic load conditions. Conventional LTE channel access does not provide any improvement in throughput or delay over these two schemes for small message transmissions.