A path-dependent option in which the payoff depends only on one event or piece of information. A good example is a barrier option because its payoff depends at any point in time on whether the underlying asset traded at or through the barrier level or not. Similarly, a lookback option is a soft path-dependent option because its payoff depends on the extremum, i.e., the higher or lowest level attained by the underlying over the life of the option.

This type of option is also known a soft path-dependent option.

The opposite of a memoryless path-dependent option is a path-dependent option with strong memory.