The present disclosure is directed toward a semi-compliant to non-compliant, conformable balloon useful in medical applications. Conformable balloons of the present disclosure exhibit a low or insignificant straightening force when in a curved configuration and at inflation pressures greater than 4 atm. Balloons of the present disclosure are constructed of material that can compress along an inner length when the balloon is in a curved configuration. In further embodiments, balloons of the present disclosure can be constructed of material that sufficiently elongates along an outer arc when the balloon is in a curved configuration. As a result, medical balloons, in accordance with the present disclosure, when inflated in a curved configuration, exhibit kink-free configurations and do not cause a significant degree of vessel straightening.