DNA is emerging as an increasingly attractive medium for data storage due to a number of important and unique advantages it offers, most notably the unprecedented durability and density. While the technology is evolving rapidly, the prohibitive cost of reads and writes, the high frequency and the peculiar nature of errors occurring in DNA storage pose a significant challenge to its adoption. In this work we make a novel observation that the probability of successful recovery of a given bit from any type of a DNA-based storage system highly depends on its physical location within the DNA molecule. In other words, when used as a storage medium, some parts of DNA molecules appear significantly more reliable than others. We show that large differences in reliability between different parts of DNA molecules lead to highly inefficient use of error-correction resources, and that commonly used techniques such as unequal error-correction cannot be used to bridge the reliability gap between different locations in the context of DNA storage. We then propose two approaches to address the problem. The first approach is general and applies to any types of data; it stripes the data and ECC codewords across DNA molecules in a particular fashion such that the effects of errors are spread out evenly across different codewords and molecules, effectively de-biasing the underlying storage medium. The second approach is application-specific, and seeks to leverage the underlying reliability bias by using application-aware mapping of data onto DNA molecules such that data that requires higher reliability is stored in more reliable locations, whereas data that needs lower reliability is stored in less reliable parts of DNA molecules. We show that the proposed data mapping can be used to achieve graceful degradation in the presence of high error rates, or to implement the concept of approximate storage in DNA.