If your partner likes the idea of being lulled to sleep by music OT a podcast and you're more interested in complete silence, there's not a lot you can do other than resign yourself to a restless, interrupted sleep or force your partner to resort to sleeping with headphones in. Neither situation is especially ideal.
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Luckily, there's a solution to this problem. For 30, you could buy your partner a pair of Sleep Phones. These headband-like devices incorporate two discreet speakers, which pipe music directly into the wearer's ears, and the shortened cable ensures that there's absolutely no chance of anyone being garroted in their sleep by mistake. Comfortable and discreet, Sleep Phones are machine-washable, available in a variety of colors and sizes from extra-small to extra-large, although the medium is likely to be enough for most people.

If you're feeling particularly affluent, you might also want to take advantage of the cable-free Bluetooth version, which is available for the considerably higher price of 69.99 but might well be worth it as an alternative to tucking your phone under your pillow overnight!