Context : The source spectrum of cosmic rays is not well determined by diffusive shock acceleration models .
The propagated fluxes of proton , helium , and heavier primary cosmic-ray species ( up to Fe ) are a means to indirectly access it .
But how robust are the constraints , and how degenerate are the source and transport parameters ?

Aims : We check the compatibility of the primary fluxes with the transport parameters derived from the B/C analysis , but also ask whether they add further constraints .
We study whether the spectral shapes of these fluxes and their ratios are mostly driven by source or propagation effects .
We then derive the source parameters ( slope , abundance , and low-energy shape ) .

Methods : Simple analytical formulae are used to address the issue of degeneracies between source/transport parameters , and to understand the shape of the p/He and C/O to Fe/O data .
The full analysis relies on the USINE propagation package , the MINUIT minimisation routines ( \chi ^ { 2 } analysis ) and a Markov Chain Monte Carlo ( MCMC ) technique .

Results : Proton data are well described in the simplest model defined by a power-law source spectrum and plain diffusion .
They can also be accommodated by models with , e.g. , convection and/or reacceleration .
There is no need for breaks in the source spectral indices below \sim 1 TeV/n .
Fits to the primary fluxes alone do not provide physical constraints on the transport parameters .
If we leave the source spectrum free , parametrised by the form dQ / dE = q \beta ^ { \eta _ { S } } { \cal R } ^ { - \alpha } , and fix the diffusion coefficient K ( R ) = K _ { 0 } \beta ^ { \eta _ { T } } { \cal R } ^ { \delta } so as to reproduce the B/C ratio , the MCMC analysis constrains the source spectral index \alpha to be in the range 2.2 - 2.5 for all primary species up to Fe , regardless of the value of the diffusion slope \delta .
The values of the parameter \eta _ { S } describing the low-energy shape of the source spectrum are degenerate with the parameter \eta _ { T } describing the low-energy shape of the diffusion coefficient : we find \eta _ { S } - \eta _ { T } \approx 0 for p and He data , but \eta _ { S } - \eta _ { T } \approx 1 for C to Fe primary species .
This is consistent with the toy-model calculation in which the shape of the p/He and C/O to Fe/O data is reproduced if \eta _ { S } - \eta _ { T } \approx 0 - 1 ( no need for different slopes \alpha ) .
When plotted as a function of the kinetic energy per nucleon , the low-energy p/He ratio is determined mostly by the modulation effect , whereas primary/O ratios are mostly determined by their destruction rate .

Conclusions : Models based on fitting B/C are compatible with primary fluxes .
The different spectral indices for the propagated primary fluxes up to a few TeV/n can be naturally ascribed to transport effects only , implying universality of elemental source spectra .