diff --git a/doc/reference/c++/gf/fourier.rst b/doc/reference/c++/gf/fourier.rst
index 1d60835a..f86da8ac 100644
--- a/doc/reference/c++/gf/fourier.rst
+++ b/doc/reference/c++/gf/fourier.rst
@@ -22,11 +22,19 @@ Synopsis
  gf<imfreq, Target, Opt> make_gf_from_fourier(gf<imtime, Target, Opt>            const&);
  gf<imfreq, Target, Opt> make_gf_from_fourier(gf_view<imtime, Target, Opt>       const&);
  gf<imfreq, Target, Opt> make_gf_from_fourier(gf_const_view<imtime, Target, Opt> const&);
- 
+
+ gf<imfreq, Target, Opt> make_gf_from_fourier(gf<imtime, Target, Opt>            const&, int n_iw);
+ gf<imfreq, Target, Opt> make_gf_from_fourier(gf_view<imtime, Target, Opt>       const&, int n_iw);
+ gf<imfreq, Target, Opt> make_gf_from_fourier(gf_const_view<imtime, Target, Opt> const&, int n_iw);
+  
  gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf<imfreq, Target, Opt>            const&);
  gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf_view<imfreq, Target, Opt>       const&);
  gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf_const_view<imfreq, Target, Opt> const&);
 
+ gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf<imfreq, Target, Opt>            const&, int n_tau);
+ gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf_view<imfreq, Target, Opt>       const&, int n_tau);
+ gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf_const_view<imfreq, Target, Opt> const&, int n_tau);
+
 
 **fourier, inverse_fourier**
 
@@ -57,10 +65,7 @@ We therefore use *a view* as LHS::
 **make_gf_from_fourier, make_gf_from_inverse_fourier**
 
 In the case where we want to create a *new* container from the fourier transform of gt, 
-we can use the function make_gf_from_fourier, in which choice is explicitly made to generate a new gf with the same number of points in the mesh.
-(Cf example below).
-
-DOC TO BE FINISHED.
+we can use the function make_gf_from_fourier.
 
 Example
 =========
diff --git a/doc/reference/c++/gf/fourier_0.cpp b/doc/reference/c++/gf/fourier_0.cpp
index defa4549..9f9ba97a 100644
--- a/doc/reference/c++/gf/fourier_0.cpp
+++ b/doc/reference/c++/gf/fourier_0.cpp
@@ -3,17 +3,16 @@ using namespace triqs::gfs;
 int main() {
  double beta = 1, a = 1;
  int N = 10000;
- auto gw = gf<imfreq>{{beta, Fermion, N}, {1, 1}};
+ auto gw = gf<imfreq>{{beta, Fermion, N/2}, {1, 1}};
  auto gt = gf<imtime>{{beta, Fermion, N}, {1, 1}};
 
  triqs::clef::placeholder<0> om_;
  gw(om_) << 1 / (om_ - a);
 
  // fills a full *view* of gt with the contents of the FFT
- // NB : the mesh of gt *must* have the same size as the mesh of gw.
  gt() = inverse_fourier(gw);
 
- // make a new fresh gf, with the same size mesh, from the FFT of gt
- auto gw2 = make_gf_from_fourier(gt);
+ // make a new fresh gf from the FFT of gt with a mesh of size N/2
+ auto gw2 = make_gf_from_fourier(gt, N/2);
 }
 
diff --git a/doc/reference/python/green/tail.rst b/doc/reference/python/green/tail.rst
index b1fd2a54..21f0d727 100644
--- a/doc/reference/python/green/tail.rst
+++ b/doc/reference/python/green/tail.rst
@@ -44,17 +44,13 @@ Basic ``TailGf`` object
 
     from pytriqs.gf.local import *
     
-    t = TailGf(shape=(1,1))
+    t = TailGf(N1=1, N2=1)
     print "t = ",t
     print "t.data.shape = ",t.data.shape
     print "t.order_min = ",t.order_min
     print "t.order_max = ",t.order_max
     print "t.mask = ",t.mask
     print "t[1] = ",t[1]
-    t[1]=[1]
-    print "t = ",t
-    t[-1]=.25
-    print "t = ",t
     print "t(100) = ",t(100)
 
 
@@ -101,6 +97,7 @@ coefficients :math:`(\mathbf{a}_{-1})_{00} = 0`\ ,
 .. runblock:: python
 
     from pytriqs.gf.local import *
+    import numpy
     g = GfImFreq(indices = [1], beta = 50, n_points = 1000, name = "imp")
     g <<= inverse( iOmega_n + 0.5 )
     g.tail.zero()
diff --git a/triqs/gfs/local/fourier_matsubara.hpp b/triqs/gfs/local/fourier_matsubara.hpp
index 86943f05..f4880aa1 100644
--- a/triqs/gfs/local/fourier_matsubara.hpp
+++ b/triqs/gfs/local/fourier_matsubara.hpp
@@ -49,30 +49,32 @@ namespace gfs {
  void triqs_gf_view_assign_delegation(gf_view<imfreq, matrix_valued, no_tail> g,
                                       gf_keeper<tags::fourier, imtime, matrix_valued, no_tail> const& L);
 
- template <typename Opt> gf_mesh<imfreq, Opt> make_mesh_fourier_compatible(gf_mesh<imtime, Opt> const& m) {
-  int L = (m.size() - (m.kind() == full_bins ? 1 : 0))/2;
-  return {m.domain(), L};
- }
-
- template <typename Opt>
- gf_mesh<imtime, Opt> make_mesh_fourier_compatible(gf_mesh<imfreq, Opt> const& m, mesh_kind mk = full_bins) {
-  int L = 2*m.size() + (mk == full_bins ? 1 : 0);
-  return {m.domain(), L};
- }
-
  template <typename Target, typename Opt, bool V, bool C>
- gf<imfreq, Target, Opt> make_gf_from_fourier(gf_impl<imtime, Target, Opt, V, C> const& gt) {
-  auto gw = gf<imfreq, Target, Opt>{make_mesh_fourier_compatible(gt.mesh()), get_target_shape(gt)};
+ gf<imfreq, Target, Opt> make_gf_from_fourier(gf_impl<imtime, Target, Opt, V, C> const& gt, int n_iw) {
+  auto m = gf_mesh<imfreq, Opt>{gt.mesh().domain(), n_iw};
+  auto gw = gf<imfreq, Target, Opt>{m, get_target_shape(gt)};
   gw() = fourier(gt);
   return gw;
  }
 
  template <typename Target, typename Opt, bool V, bool C>
- gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf_impl<imfreq, Target, Opt, V, C> const& gw, mesh_kind mk = full_bins) {
-  auto gt = gf<imtime, Target, Opt>{make_mesh_fourier_compatible(gw.mesh(), mk), get_target_shape(gw)};
+ gf<imfreq, Target, Opt> make_gf_from_fourier(gf_impl<imtime, Target, Opt, V, C> const& gt) {
+  return make_gf_from_fourier(gt, (gt.mesh().size() - (gt.mesh().kind() == full_bins ? 1 : 0)) / 2);
+ }
+
+ template <typename Target, typename Opt, bool V, bool C>
+ gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf_impl<imfreq, Target, Opt, V, C> const& gw, int n_tau,
+                                                      mesh_kind mk = full_bins) {
+  auto m = gf_mesh<imtime, Opt>{gw.mesh().domain(), n_tau};
+  auto gt = gf<imtime, Target, Opt>{m, get_target_shape(gw)};
   gt() = inverse_fourier(gw);
   return gt;
  }
+
+ template <typename Target, typename Opt, bool V, bool C>
+ gf<imtime, Target, Opt> make_gf_from_inverse_fourier(gf_impl<imfreq, Target, Opt, V, C> const& gw, mesh_kind mk = full_bins) {
+  return make_gf_from_inverse_fourier(gw, 2 * gw.mesh().size() + (mk == full_bins ? 1 : 0), mk);
+ }
 }
 
 namespace clef {