We describe two studies designed to characterize the total column densities , kinetic energies , and acceleration physics of broad absorption line ( BAL ) outflows in quasars . The first study uses new Chandra X-ray and ground-based rest-frame UV observations of 7 quasars with mini-BALs at extreme high speeds , in the range 0.1 c to 0.2 c , to test the idea that strong radiative shielding ( and therefore strong X-ray absorption ) is needed to moderate the mini-BAL ionizations and facilitate their acceleration to extreme speeds . We find that the X-ray absorption is weak or absent , with generally N _ { H } < { few } \times 10 ^ { 22 } cm ^ { -2 } , and that radiative shielding is not important . We argue that the mini-BAL ionizations are controlled , instead , by high gas densities of order n _ { H } \sim 4 \times 10 ^ { 8 } cm ^ { -3 } in small outflow substructures . If we conservatively assume that the total column density in the mini-BAL gas is N _ { H } < 10 ^ { 22 } cm ^ { -2 } , covering > 15 % of the UV continuum source along our lines of sight ( based on measured line depths ) , then the radial thickness of these outflows is only \Delta R < 3 \times 10 ^ { 13 } cm and their transverse size is > 8 \times 10 ^ { 15 } cm . Thus the outflow regions have the shape of very thin “ pancakes ” viewed face-on , or they occupy larger volumes like a spray of dense cloudlets with a very small volume filling factor . We speculate that this situation ( with ineffective shielding and small dense outflow substructures ) applies to most quasar outflows , including BALs . Our second study focuses from BALs of low-abundance ions , mainly PV 1118,1128 Å , whose significant strengths imply large column densities , N _ { H } > 10 ^ { 22 } cm ^ { -2 } , that can further challenge models of the outflow acceleration . In spite of the difficulties of finding this line in the Ly \alpha forest , a search through the SDSS DR9 quasar catalog reveals > 50 BAL sources at redshifts z > 2.3 with strong PV BALs , which we are now using to characterize the general properties of high-column outflows .