Step 1: Frame the goal. A young woman with heavy periods usually still wants to keep her uterus and fertility, so the ideal option must control bleeding while being conservative and reversible.
Step 2: Look at the copper devices. Both the Cu IUD and the NOVA T copper coil are known to make menstrual flow heavier, so prescribing them for menorrhagia would aggravate the very problem we are treating. They are ruled out.
Step 3: Hysterectomy ends bleeding permanently but it is major surgery that sacrifices the uterus, so it is kept for resistant cases or when childbearing is complete, not for routine first-line care. That leaves combined oral contraceptive pills, which thin the endometrium, steady the cycle and cut blood loss substantially, all while offering contraception.
Step 4: The conservative, fertility-sparing and effective first choice for menorrhagia in the reproductive years is OCPs.
\[\boxed{\text{OCPs}}\]