Numerous medium access control (MAC) have been proposed for Low-power Lossy Networks (LLNs) over the recent years. They aim at ensuring both energy efficiency and robustness of the communication transmissions. Nowadays, we observe deployments of LLNs for potentially critical application scenarios (e.g., plant monitoring, building automation), which require both determinism and security guarantees. They involve battery-powered devices which communicate over lossy wireless links. Radio interfaces are turned off by a node as soon as no traffic is to be sent or relayed. Denial-of-sleep attacks consist in exhausting the devices by forcing them to keep their radio on. We here focus on jamming attacks whose impact can be mitigated by approaches such as time-division and channel hopping techniques. We use the IEEE 802.15.4e standard to show that such approaches manage to be resistant to jamming but yet remain vulnerable to selective jamming. We discuss the potential impacts of such onslaughts, depending on the knowledge gained by the attacker, and to what extent envisioned protections may allow jamming attacks to be handled at upper layers.