Periodic configurations, or oscillators, occur in many cellular
automata. In an oscillator, repeated applications of the automaton
rules eventually restore the configuration to its initial state. This
paper considers oscillators in Conway's Life; analogous techniques
should apply to other rules. Three explicit methods are presented to
construct oscillators in Life while guaranteeing certain complexity
bounds, leading to the existence of
\begin{itemize}
\item
an infinite sequence $K_n$ of oscillators of periods
$n=58$, 59, 60, \dots \ and uniformly bounded population, and
\item
an infinite sequence $D_n$ of oscillators of periods $n=58$, 59, 60,
\dots \ and diameter bounded by $b \sqrt{\log n}$, where $b$ is a
uniform constant.
\end{itemize}
The proofs make use of the first explicit example of a stable
glider reflector in Life, solving a longstanding open question about
this cellular automaton.