Femtosecond laser direct-writing is an attractive technique to fabricate fiber Bragg gratings and to achieve through-the-coating inscription. In this article, we report the direct inscription of high-quality first-order gratings in optical fiber, without the use of an index-matching medium. A new alignment technique based on the inscription of weak probe gratings is used to track the relative position between the focal spot and fiber core. A simple and flexible method to precisely control the position of each grating plane is also presented. With this method, periodic phase modulation of grating structures is achieved and used to inscribe arbitrary apodization and phase profiles. It is shown that a burst of multiple laser pulses used to inscribe each grating plane leads to a significant increase in the grating strength, while maintaining low insertion loss, critical for many applications.