The energetic and economic attractiveness of linear solar concentrators can be significantly improved by the use of properly secondary non-imaging (CPC-type) concentrators. Two specific illustrative cases are analyzed. One is the optical re-design of a commercial two-stage solar concentrator which generates process steam at 150 degree(s)C. The primary is a linear Fresnel reflector with one-axis horizontal tracking. The receiver is a stationary, non- evacuated, glazed tubular receiver with secondary CPC. We have re-designed the initial, manufacturer-designed secondary so as to noticeably improve collector thermal output. Details of secondary design and system performance are presented. The other is a new concept in secondary CPC-type concentrators for parabolic trough collectors with tubular receivers and large rim angles (typically 80 degree(s)-120 degree(s)). It had been though that such large-rim- angle concentrators could not benefit from secondary concentrators, since the second-stage concentration boost goes as 1/sin(rim angle). However, by introducing multiple asymmetric CPC-type devices, we can increase the geometric concentration of a 90 degree(s) rim angle parabolic trough by roughly a factor of 3. Furthermore, certain secondary designs can be accommodated within the annulus of currently-manufactured evacuated receiver tubes, and still offer a flux concentration improvement of about a factor of 2.5. Examples of the new secondary designs, and achievable concentration gains, are presented.