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A read from 454 or Ion Torrent sequencers is natively represented as a flowgram, which is a sequence of pairs of a nucleotide and its (fractional) intensity. Recent work has focused on improving the accuracy of base calling (conversion of flowgrams to DNA sequences) in order to facilitate read mapping and downstream analysis of sequence variants. However, base calling always incurs a loss of information by discarding fractional intensity information. We argue that base calling can be avoided entirely by directly aligning the flowgrams to DNA sequences. We introduce an algorithm for flowgram-string alignment based on dynamic programming, but covering more cases than standard local or global sequence alignment. We also propose a scoring scheme that takes into account sequence variations (from substitutions, insertions, deletions) and sequencing errors (flow intensities contradicting the homopolymer length) separately. This allows to resolve fractional intensities, ambiguous homopolymer lengths and editing events at alignment time by choosing the most likely read sequence given both the nucleotide intensities and the reference sequence. We provide a proof-of-concept implementation and demonstrate the advantages of flowgram-string alignment compared to base-called alignments.