Do I Need An Allergy Resistant Pillow Cover With An Allergy Resistant Pillow?

I bought a pillow that is specially designed to protect against allergans. Should I put my regular pillow cover on it or should I buy an allergy resistant pillow cover? Or should I use a pillow cover at all. Thanks.

Aller Ease Classic Allergen Barrier Pillow Cover, Set of 2

Amazon.com The Aller-Ease Classic cover for standard-sized pillows offers a barrier that effectively blocks common household allergens such as microscopic particles, dust mites and pollen that inhabit pillows. Made with a polypropylene non-woven fabric with polyethylene lamination, the waterproof Classic cover traps dust and mites inside while letting moisture vapor out. It features a zippered [...]

Aller Ease Cotton Allergen Barrier Pillow Cover, Set of 2

Amazon.com The Aller-Ease Cotton cover for standard-sized pillows offers a barrier that effectively blocks common household allergens. The 100 percent tightly-woven cotton construction provides excellent protection from microscopic particles and pollen, while at the same time providing the benefits of a cool, breathable fabric for a more comfortable night’s sleep. It does not trap body [...]