A method of seismic exploration above a region of the subsurface of the earth containing structural or stratigraphic features conducive to the presence, migration, or accumulation of hydrocarbons, the method comprising: (a) selecting a controllable source comprising a housing and a piston located within said housing for generating a sweep signal; (b) selecting a plurality of parameters characteristic of said controllable source, wherein said plurality of parameters comprise at least: a maximum piston displacement value, a maximum piston velocity value, and a maximum piston acceleration value; (c) determining limit curves for each of said plurality of parameters as a function of frequency, wherein said limit curves comprise: a displacement limit curve calculated based on said maximum piston displacement value, a velocity limit curve calculated based on said maximum piston velocity value, and an acceleration limit curve calculated based on said maximum piston acceleration value, and wherein each of said limit curves is based on a volume acceleration constraint; (d) using said determined limit curves to obtain a constraint curve for said controllable source; (e) determining from said constraint curve a sweep signal for said controllable source; and, (f) using said sweep signal in conjunction with said controllable source to collect seismic data proximate to a region of the subsurface of the earth as part of a sweep profile in which the controllable source operates at or near a maximum acoustic power output of the controllable source by running the controllable source at a maximum output level capable by the controllable source, wherein operating the controllable source at or near the maximum acoustic power output minimizes a duration of the sweep or maximizes an achievable amplitude for a target frequency profile when the sweep has a given allowed sweep duration. (a) selecting a controllable source comprising a housing and a piston located within said housing for generating a sweep signal; (b) selecting a plurality of parameters characteristic of said controllable source, wherein said plurality of parameters comprise at least: a maximum piston displacement value, a maximum piston velocity value, and a maximum piston acceleration value; a maximum piston displacement value, a maximum piston velocity value, and a maximum piston acceleration value; (c) determining limit curves for each of said plurality of parameters as a function of frequency, wherein said limit curves comprise: a displacement limit curve calculated based on said maximum piston displacement value, a velocity limit curve calculated based on said maximum piston velocity value, and an acceleration limit curve calculated based on said maximum piston acceleration value, and wherein each of said limit curves is based on a volume acceleration constraint; a displacement limit curve calculated based on said maximum piston displacement value, a velocity limit curve calculated based on said maximum piston velocity value, and an acceleration limit curve calculated based on said maximum piston acceleration value, and (d) using said determined limit curves to obtain a constraint curve for said controllable source; (e) determining from said constraint curve a sweep signal for said controllable source; and, (f) using said sweep signal in conjunction with said controllable source to collect seismic data proximate to a region of the subsurface of the earth as part of a sweep profile in which the controllable source operates at or near a maximum acoustic power output of the controllable source by running the controllable source at a maximum output level capable by the controllable source,