An LED strip featuring perforations between adjacent LEDs that enable one to break the LED strip at the perforation using mere hand pressure. In another aspect of the invention, not only does the LED strip feature “polarity-correcting” circuitry, but also that each LED proper contains such a polarity-correcting circuit, so that regardless of where the lighting strip is broken, the broken-off portion still features polarity-correcting qualities. In yet another aspect of the invention, the LED strip can be broken at any perforation, and the two broken surfaces will each feature electrical contacts or connectors that can be removably (temporarily) attached to a pair of electrical conductors (e.g., wires), thereby permitting each of the remaining and broken-off sections of the original LED strip to function as a light source, as well as to be able to connect to both “upstream” electrical sources and “downstream” electrical loads such as additional LED strips. Thus, such LED strips may then be manufactured and sold in standard lengths, and the customer or other end-user can easily adjust the LED strip to his or her particular application by breaking off the unwanted section at the desired location.