Local delivery of drug to some tissue sites has room for improvement, particularly with respect to extended drug delivery with minimally invasive devices. The problem is particularly acute for certain drugs, such as those having relatively low water solubility. It is desirable to provide new designs of intravesical drug delivery devices, and other implantable devices capable of delivering drugs at effective release rates for a range of different drugs. In accordance with the present invention: an implantable drug delivery device includes: a housing having a closed drug reservoir lumen bounded by a first wall structure constructed of a first material and a hydrophilic second wall structure constructed of a second material; and a drug contained in the drug reservoir lumen, wherein the first wall structure is impermeable to the drug and the second wall structure is permeable to the drug, and the durometer of the first and second materials is selected to make the device compliant in the bladder of a patient.