There is a widely shared belief in contemporary epistemology that propositional knowledge is incompatible with certain kinds of luck, most of all with so called veritic luck. A subject is veritically lucky in his or her belief that p if this belief is true not due to its foundations (for example, reasons which an agent has to believe that p) but by mere accident. The acceptance of the thesis of incompatibility of knowledge with this kind of luck led to significant modifications of a popular modern epistemological tripartite analysis of propositional knowledge according to which subject knows that p if and only if he or she believes that p is true, p is actually true, and an agent's belief that p is true is justified. In his famous paper "Is True Justified Belief Knowledge" E. Gettier demonstrated that true justified belief may not be knowledge. The core of the problem is that in the cases described by Gettier and the like an agent's belief, though justified, is true by accident. This gave rise to a set of theories introducing additional conditions of knowledge which could exclude veritic luck. In this paper the author critically discusses main modifications of the tripartite concept of knowledge aimed at making it independent on veritic luck, and show that they are unable to solve this problem. He agrees with those who think that the very thesis of incompatibility of knowledge with veritic luck is wrong. But he disagrees that all kinds of veritic luck are compatible with knowledge: the author supposes that good veritic luck is compatible with knowledge only when it compensates some negative effect of antecedent bad epistemic luck. According to this view original Gettier examples are not cases of knowledge whereas brokenclocks case and fake-barns case are. This account allows treating many classic cases of dependence of knowledge on luck as cases of knowledge-acquirement, but in the same time it excludes the inclusion into the class of knowledge such intuitively irrelevant outcomes as lucky guess and wishful thinking.