One of the most concerning threats for modern AI systems is data poisoning,\nwhere the attacker injects maliciously crafted training data to corrupt the\nsystem's behavior at test time. Availability poisoning is a particularly\nworrisome subset of poisoning attacks where the attacker aims to cause a\nDenial-of-Service (DoS) attack. However, the state-of-the-art algorithms are\ncomputationally expensive because they try to solve a complex bi-level\noptimization problem (the "hammer"). We observed that in particular conditions,\nnamely, where the target model is linear (the "nut"), the usage of\ncomputationally costly procedures can be avoided. We propose a\ncounter-intuitive but efficient heuristic that allows contaminating the\ntraining set such that the target system's performance is highly compromised.\nWe further suggest a re-parameterization trick to decrease the number of\nvariables to be optimized. Finally, we demonstrate that, under the considered\nsettings, our framework achieves comparable, or even better, performances in\nterms of the attacker's objective while being significantly more\ncomputationally efficient.\n