Conductive connections, structures with such connections, and methods of manufacture

A manufacture comprising:

• a first structure comprising one or more contact pads;
• one or more electrically conductive connections each of which has a bottom attached to at least one contact pad and comprises solder;
• and
• a first layer comprising a top surface and one or more through-holes in the top surface, each through-hole's sidewall being a dielectric sidewall, each through-hole containing at least a segment of a corresponding electrically conductive connection, the segment physically contacting the through-hole's dielectric sidewall, the electrically conductive connection being recessed in the through-hole at the top of the through-hole;
• wherein the first layer comprises:
• a first dielectric sub-layer comprising, at each electrically conductive connection, an upward protrusion protruding above the first structure and laterally surrounding and physically contacting the electrically conductive connection;
• and
• a second dielectric sub-layer overlaying the first dielectric sub-layer, the second dielectric sub-layer laterally surrounding each upward protrusion, the second dielectric sub-layer being a different material than the first dielectric sub-layer;
• wherein each electrically conductive connection physically contacts the first dielectric sub-layer but not the second dielectric sub-layer;
• and
• each electrically conductive connection and the first dielectric sub-layer are recessed in each through-hole.