This article presents a method for precise mode control of laser-written waveguides for broadband, low-dispersion 3D integrated optics. The proposed overlap-controlled multi-scan (OCMS) method enables precise control of the refractive index (RI) profile of 3D waveguides with high spatial precision in various glasses. This method allows for variable mode-field distribution, robust and broadband coupling, and demonstrates dispersionless LP21-mode conversion of supercontinuum pulses with minimal coupling ratio deviation. The OCMS method provides a route to achieve ultra-broadband and low-dispersion coupling in 3D photonic circuits, offering advantages over conventional planar waveguide-optic platforms. The OCMS method enables the fabrication of waveguides with submicron spatial resolution and RI resolution on the order of 10^-5. It allows for the creation of waveguides with various geometries and RI configurations previously unachievable with traditional femtosecond laser direct writing (FLDW). The method is applicable to various glasses, including commercial available screen glasses, and enables both positive and negative RI control. The OCMS method also allows for the arbitrary customization of laser-induced thermal modifications with high resolution, enabling submicron or nanoscale structural modifications in glasses beyond current thermal FLDW techniques. The OCMS method is demonstrated to achieve high mode circularity and low insertion loss in GRIN waveguides, with a record low insertion loss of 0.29 dB for a 10 mm long waveguide at 1550 nm. The method also enables robust and broadband coupling for mode-selective 3D waveguide couplers, achieving high mode coupling ratios and high mode purity. The OCMS-based mode coupler demonstrates uniform performance over a broadband of 110 nm centered at 1550 nm with the largest deviation <0.1 dB in coupling ratios. The OCMS method is also demonstrated to enable chip-scale mode manipulation of ultrashort laser pulses, achieving conformal transmission of ultrashort pulses with negligible distortion in the time domain. The method enables broadband supercontinuum pulse routing to a desired higher-order mode with minimal spatiotemporal distortion. The OCMS method provides a route to achieve ultra-broadband and low-dispersion coupling based on 3D glass waveguides, which has overwhelming advantages in transmitting and manipulating linear and nonlinear laser light over conventional planar waveguide-optic platforms. The OCMS method represents a significant step towards realizing large-scale 3D photonic circuits with great potential to address the scaling challenges in cutting-edge physical applications such as quantum information and 3D optical topology.This article presents a method for precise mode control of laser-written waveguides for broadband, low-dispersion 3D integrated optics. The proposed overlap-controlled multi-scan (OCMS) method enables precise control of the refractive index (RI) profile of 3D waveguides with high spatial precision in various glasses. This method allows for variable mode-field distribution, robust and broadband coupling, and demonstrates dispersionless LP21-mode conversion of supercontinuum pulses with minimal coupling ratio deviation. The OCMS method provides a route to achieve ultra-broadband and low-dispersion coupling in 3D photonic circuits, offering advantages over conventional planar waveguide-optic platforms. The OCMS method enables the fabrication of waveguides with submicron spatial resolution and RI resolution on the order of 10^-5. It allows for the creation of waveguides with various geometries and RI configurations previously unachievable with traditional femtosecond laser direct writing (FLDW). The method is applicable to various glasses, including commercial available screen glasses, and enables both positive and negative RI control. The OCMS method also allows for the arbitrary customization of laser-induced thermal modifications with high resolution, enabling submicron or nanoscale structural modifications in glasses beyond current thermal FLDW techniques. The OCMS method is demonstrated to achieve high mode circularity and low insertion loss in GRIN waveguides, with a record low insertion loss of 0.29 dB for a 10 mm long waveguide at 1550 nm. The method also enables robust and broadband coupling for mode-selective 3D waveguide couplers, achieving high mode coupling ratios and high mode purity. The OCMS-based mode coupler demonstrates uniform performance over a broadband of 110 nm centered at 1550 nm with the largest deviation <0.1 dB in coupling ratios. The OCMS method is also demonstrated to enable chip-scale mode manipulation of ultrashort laser pulses, achieving conformal transmission of ultrashort pulses with negligible distortion in the time domain. The method enables broadband supercontinuum pulse routing to a desired higher-order mode with minimal spatiotemporal distortion. The OCMS method provides a route to achieve ultra-broadband and low-dispersion coupling based on 3D glass waveguides, which has overwhelming advantages in transmitting and manipulating linear and nonlinear laser light over conventional planar waveguide-optic platforms. The OCMS method represents a significant step towards realizing large-scale 3D photonic circuits with great potential to address the scaling challenges in cutting-edge physical applications such as quantum information and 3D optical topology.