  We present a lumped-element Josephson parametric amplifier designed to
operate with strong coupling to the environment. In this regime, we observe
broadband frequency dependent amplification with multi-peaked gain profiles. We
account for this behaviour using the "pumpistor" model which allows for
frequency dependent variation of the external impedance. Using this
understanding, we demonstrate control over gain profiles through changes in the
environment impedance at a given frequency. With strong coupling to a suitable
external impedance we observe a significant increase in dynamic range, and
large amplification bandwidth up to 700 MHz giving near quantum-limited
performance.
