diff --git a/matlab/mr_hessian.m b/matlab/mr_hessian.m
index 14e7a59906c97282b34a192ff54fccd486a35d62..9f56e6d75f350e662495cdaa74d00def151358a1 100644
--- a/matlab/mr_hessian.m
+++ b/matlab/mr_hessian.m
@@ -50,12 +50,16 @@ func = str2func(func);
 [f0, ff0]=feval(func,x,varargin{:});
 n=size(x,1);
 h2=bayestopt_.ub-bayestopt_.lb;
+hmax=bayestopt_.ub-x;
+hmax=min(hmax,x-bayestopt_.lb);
 %h1=max(abs(x),gstep_*ones(n,1))*eps^(1/3);
 %h1=max(abs(x),sqrt(gstep_)*ones(n,1))*eps^(1/6);
 if isempty(h1),
     h1=max(abs(x),sqrt(gstep_)*ones(n,1))*eps^(1/4);
 end
 
+h1 = min(h1,0.5.*hmax);
+
 if htol0<htol, 
     htol=htol0;
 end
@@ -103,6 +107,7 @@ while i<n,
             else
                 h1(i)=2.1*h1(i);
             end
+            h1(i) = min(h1(i),0.5*hmax(i));
             xh1(i)=x(i)+h1(i);
 %             c=mr_nlincon(xh1,varargin{:});
 %             while c
@@ -127,7 +132,7 @@ while i<n,
         it=it+1;
         dx(it)=(fx-f0);
         h0(it)=h1(i);
-        if h1(i)<1.e-12*min(1,h2(i)),
+        if h1(i)<1.e-12*min(1,h2(i)) & h1(i)<0.5*hmax(i),
             ic=1;
             hcheck=1;
         end
diff --git a/matlab/newrat.m b/matlab/newrat.m
index 7e84595f013b1555f2ec784628f74f55a0973037..87d353bfb4858fef7c662eecde9938f9bfca7549 100644
--- a/matlab/newrat.m
+++ b/matlab/newrat.m
@@ -1,7 +1,7 @@
 function [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit, flagg, varargin)
 %  [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit, flagg, varargin)
 %
-%  Optimiser with outer product gradient and 'Gibbs type' steps
+%  Optimiser with outer product gradient and with sequences of univariate steps
 %  uses Chris Sims subroutine for line search
 %
 %  func0 = name of the function
@@ -125,9 +125,9 @@ while norm(gg)>gtol & check==0 & jit<nit,
         nig=[nig ig];
          if (fval-fvala)<gibbstol*(fval0(icount)-fval),
              igibbs=0;
-             disp('Last Gibbs step, gain too small!!')
+             disp('Last sequence of univariate step, gain too small!!')
          else
-            disp('Gibbs step!!')
+            disp('Sequence of univariate steps!!')
         end
         fval=fvala;
     end