Here's why:

* Acid-fastness is a property related to the cell wall of bacteria, specifically the presence of mycolic acids which make them resistant to decolorization by acids.

* Coccobacillus refers to the shape of a bacterium, which is somewhere between a coccus (round) and a bacillus (rod-shaped).

Examples of acid-fast coccobacilli include:

* Mycobacterium leprae (Leprosy): This bacterium is responsible for leprosy and is often described as having a "dimorphic" morphology, meaning it can appear as both cocci and bacilli.

* Mycobacterium tuberculosis (Tuberculosis): While primarily rod-shaped, M. tuberculosis can occasionally exhibit coccobacillus forms, especially under certain growth conditions.

Important Note: Acid-fast staining is a useful technique for identifying bacteria with high mycolic acid content, regardless of their exact shape.