We introduce Scallop, an accurate reference-based transcript assembler that improves reconstruction of multi-exon and lowly expressed transcripts. Scallop preserves long-range phasing paths extracted from reads, while producing a parsimonious set of transcripts and minimizing coverage deviation. On 10 human RNA-seq samples, Scallop produces 34.5% and 36.3% more correct multi-exon transcripts than StringTie and TransComb, and respectively identifies 67.5% and 52.3% more lowly expressed transcripts. Scallop achieves higher sensitivity and precision than previous approaches over a wide range of coverage thresholds.