The mechanical anisotropy of Fused Deposition Modeling (FDM) fabricated parts due to voids and non-uniform bond formation between rasters represents a major challenge for the widespread adoption of this fabrication technique. The present article addresses a novel post-processing procedure for FDM Ultem™ 9085 parts based on thermal annealing coupled with isostatic pressing to produce specimens with improved mechanical and surface properties. Response surface methodology was used to obtain mathematical models for all the studied responses. In particular, the sequentiality of Doehlert Designs was exploited to select the optimal combination of time and temperature of the process, resulting in specimens with noticeably improved layer adhesion, as noted by enhancements in flexural modulus, flexural strength, strain at flexural strength, and surface roughness. Confirmatory experiences of the optimal point with different printing orientations have demonstrated the capability of the proposed method to reduce anisotropy in the mechanical properties of the treated parts. In addition, microscopy imaging, Raman spectroscopy, and X-ray diffraction were beneficial to justify the observed results. This study sheds new light on the post-processing of FDM polymers, and the presented optimization methodology can be extrapolated to other materials and processes.