An Internet of things (IoT) network is a distributed set of “smart” sensors, interconnected via a radio channel. The basic method of accessing the radio channels for these networks is Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA), in which access is carried out on the basis of contention, and confirmation of the correct reception of the packet is achieved using a receipt. If the sizes of information packets are small and comparable to the sizes of receipts, then the transmission of receipts requires a significant bandwidth of the channel, which reduces the efficiency of the network. This problem exists not only for IoT networks but also for monitoring systems, operational management of fast processes, telemetry, short messaging and many other applications. Therefore, an urgent task is to develop effective methods of multiple random access in the transmission of short information packets, the size of which is comparable to the size of receipts. To solve this problem, the authors proposed modifications of CSMA/CA random access in which, when packet collisions are detected, a diagnostic message (DM) is generated and transmitted in the broadcast mode. Based on simulation modeling, it is shown that in a wide range of network loads, the proposed random access options provide an increase in network capacity (the number of connected subscribers) of 1.5–2 times compared to the basic CSMA/CA access method when the size of the information packet is an order of magnitude larger than the size of receipts. The variant of access without acknowledgment is also considered, in which, as shown by the simulation results, at sufficiently large loads, the network can go into an unstable state.