closed-back headphones

Closed-back headphones tend to be able to produce stronger low frequencies than open-back headphones.

Semi-open headphones, have a design that can be considered as a compromise between open-back headphones and closed-back headphones.

The headphone types that provide most attenuation are in-ear canal headphones and closed-back headphones, both circumaural and supra aural.

There are also plenty of excellent-sounding closed-back headphones for less then half the money, like the Sony MDR7506 or the Audio-Technica ATH-M50s.