A device suitable for treating subcutaneous adipose tissue, comprising: a. an ultrasonic transducer for generation of ultrasonic vibrations having a proximal face and a distal face; and b. a sonotrode including a narrower proximal stem portion defining a sonotrode axis and a broader distal cap portion wherein said stem portion has a distal end and bears a proximal face of said sonotrode, said sonotrode acoustically coupled to said distal face of said ultrasonic transducer through said proximal face of said sonotrode, wherein said cap portion has a proximally-facing back side, a distal working face of said sonotrode and a periphery, wherein said distal end of said stem portion meets said back side of said cap portion, wherein where said distal end of said stem portion meets said back side of said cap portion a cross sectional area of said cap portion perpendicular to said sonotrode axis is not less than 8 times greater than a cross sectional area of said distal end of said stem portion perpendicular to said sonotrode axis; and wherein said cap portion is thin, being not less than than 2 mm and not more than 10 mm thick, wherein not less than 70% of both said working face and said back side of said cap portion are planar and perpendicular to said sonotrode axis, and wherein a periphery of said cap portion when viewed from the side is a straight line parallel to said sonotrode axis, optionally where an edge of said periphery is not a right angle, wherein said sonotrode is configured, for a selected ultrasonic frequency, to act as an acoustic amplitude transformer for both longitudinal and transverse vibration, so as simultaneously transdermally induce substantial ultrasonic transverse vibrations and substantial ultrasonic longitudinal vibrations in a volume of subcutaneous tissue through skin with which said working face is acoustically coupled. a. an ultrasonic transducer for generation of ultrasonic vibrations having a proximal face and a distal face; and b. a sonotrode including a narrower proximal stem portion defining a sonotrode axis and a broader distal cap portion wherein said stem portion has a distal end and bears a proximal face of said sonotrode, said sonotrode acoustically coupled to said distal face of said ultrasonic transducer through said proximal face of said sonotrode, wherein said cap portion has a proximally-facing back side, a distal working face of said sonotrode and a periphery, wherein said distal end of said stem portion meets said back side of said cap portion, wherein where said distal end of said stem portion meets said back side of said cap portion a cross sectional area of said cap portion perpendicular to said sonotrode axis is not less than 8 times greater than a cross sectional area of said distal end of said stem portion perpendicular to said sonotrode axis; and wherein said cap portion is thin, being not less than than 2 mm and not more than 10 mm thick, wherein not less than 70% of both said working face and said back side of said cap portion are planar and perpendicular to said sonotrode axis, and wherein a periphery of said cap portion when viewed from the side is a straight line parallel to said sonotrode axis, optionally where an edge of said periphery is not a right angle, wherein said sonotrode is configured, for a selected ultrasonic frequency, to act as an acoustic amplitude transformer for both longitudinal and transverse vibration, so as simultaneously transdermally induce substantial ultrasonic transverse vibrations and substantial ultrasonic longitudinal vibrations in a volume of subcutaneous tissue through skin with which said working face is acoustically coupled. wherein said stem portion has a distal end and bears a proximal face of said sonotrode, said sonotrode acoustically coupled to said distal face of said ultrasonic transducer through said proximal face of said sonotrode, wherein said cap portion has a proximally-facing back side, a distal working face of said sonotrode and a periphery, wherein said distal end of said stem portion meets said back side of said cap portion, wherein where said distal end of said stem portion meets said back side of said cap portion a cross sectional area of said cap portion perpendicular to said sonotrode axis is not less than 8 times greater than a cross sectional area of said distal end of said stem portion perpendicular to said sonotrode axis; and wherein said cap portion is thin, being not less than than 2 mm and not more than 10 mm thick, wherein not less than 70% of both said working face and said back side of said cap portion are planar and perpendicular to said sonotrode axis, and wherein a periphery of said cap portion when viewed from the side is a straight line parallel to said sonotrode axis, optionally where an edge of said periphery is not a right angle, wherein said sonotrode is configured, for a selected ultrasonic frequency, to act as an acoustic amplitude transformer for both longitudinal and transverse vibration, so as simultaneously transdermally induce substantial ultrasonic transverse vibrations and substantial ultrasonic longitudinal vibrations in a volume of subcutaneous tissue through skin with which said working face is acoustically coupled.