HEPA Filter
This is an absolute must. HEPA filters are proven to remove airborne allergies better than other, cheaper filters. They are also less expensive than the more "advanced" filters which in all likelihood are overkill for keeping allergens out of your bedroom air.
Sq. Ft. Coverage
Measure your bedroom before clicking "buy"! The unit you'll need will tell you how much square footage it can clean efficiently, so choose your air purifier accordingly. If your bedroom has high ceilings or is drafty, buy one with a bit more coverage space than what your room is, just to make sure that your air is getting cleaned sufficiently to prevent your seasonal allergies.
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