A portion of a conductive layer (310, 910) provides a capacitor electrode (310.0, 910.0). Dielectric trenches (410, 414, 510) are formed in the conductive layer to insulate the capacitor electrode from those portions of the conductive layer which are used for conductive paths passing through the electrode but insulated from the electrode. Capacitor dielectric (320) can be formed by anodizing tantalum while a nickel layer (314) protects an underlying copper (310) from the anodizing solution. This protection allows the tantalum layer to be made thin to obtain large capacitance. Chemical mechanical polishing of a layer (610) is made faster, and hence possibly less expensive, by first patterning the layer photolithographically to form, and/or increase in height, upward protrusions of this layer.