  We present three high finesse tunable monolithic fiber Fabry-Perot cavities
(FFPCs) with high passive mechanical stability. The fiber mirrors are fixed
inside slotted glass ferrules, which guarantee an inherent alignment of the
resonators. An attached piezoelectric element enables fast tuning of the FFPC
resonance frequency over the entire free-spectral range for two of the designs.
Stable locking of the cavity resonance is achieved for feedback bandwidths as
low as $20\,$mHz, demonstrating the high passive stability. At the other limit,
locking bandwidths up to $27\,$kHz, close to the first mechanical resonance,
can be obtained. The root-mean-square frequency fluctuations are suppressed
down to $\sim 2\,$% of the cavity linewidth. Over a wide frequency range, the
frequency noise is dominated by the thermal noise limit of the system's
mechanical resonances. The demonstrated small footprint devices can be used
advantageously in a broad range of applications like cavity-based sensing
techniques, optical filters or quantum light-matter interfaces.
