When we compare two algorithms, complexity and efficiency are often thought of as almost the same, implying that low complexity indicates good efficiency. However, these two concepts are actually distinct. We provide theoretical reasons and a few examples to demonstrate that an algorithm can be both more complex and more efficient than another at the same time. We also address several common misconceptions about iterative optimization. Problem size Time complexity - Thanks: To my colleague and friend Mohamed G. Omran for our fruitful discussions. Even though he doesn't agree with all my conclusions!