Although virtually any installed PID controller encompasses a derivative filter, and very frequently takes the standard ISA form, many tuning rules refer to the ideal controller structure, which is subsequently made realizable by introducing the so-called "derivative filter" a posteriori. Doing so can sometimes lead to undesired results. This paper investigates the matter and discusses two very simple but rigorous procedures to extend ideal PID tuning rules to the ISA controller. A benchmark simulation campaign, referring to several well-assessed rules, demonstrates the opportunity and efficacy of the proposed extensions. A quite realistic test referring to a typical process control case is also presented.