Flap endonuclease 1 (FEN1) participates in removal of RNA primers of Okazaki fragments, several DNA repair pathways, and genome stability maintenance. Defects in yeast FEN1 produce chromosomal instability, hyper-recombination, and sequence duplication. These occur because flaps produced during replication are not promptly removed. Long-lived flaps sustain breaks and form misaligned bubble structures that produce duplications. Flaps that can form secondary structure inhibit even wild-type FEN1 and are more likely to form bubbles. Although proliferating cell nuclear antigen stimulates FEN1, it cannot resolve secondary structures. Bloom protein (BLM) is a 3'-5' helicase, mutated in Bloom syndrome. BLM has been reported to interact with and stimulate FEN1 independent of helicase function. We found activation of the helicase by ATP did not alter BLM stimulation of cleavage of unstructured flaps. However, BLM stimulation of FEN1 cleavage of foldback flaps, bubbles, or triplet repeats was increased by an additional increment when ATP was added. Helicase-dependent stimulation of FEN1 cleavage was robust over a range of sizes of the single-stranded part of bubbles. However, increasing the length of the 5' annealed region of the bubble ultimately counteracted the stimulatory capacity of the BLM helicase. Moderate helicase-dependent stimulation was observed with both fixed and equilibrating CTG flaps. Our results suggest that BLM suppresses genome instability by aiding FEN1 cleavage of structure-containing flaps.