diff --git a/matlab/optimization/dynare_minimize_objective.m b/matlab/optimization/dynare_minimize_objective.m
index a4aff3bfa..79a02ef9f 100644
--- a/matlab/optimization/dynare_minimize_objective.m
+++ b/matlab/optimization/dynare_minimize_objective.m
@@ -244,7 +244,7 @@ switch minimizer_algorithm
         Save_files = 0; 
         Verbose = 0;
     end    
-    [opt_par_values,hessian_mat,gg,fval,invhess] = newrat(objective_function,start_par_value,analytic_grad,crit,nit,0,Verbose, Save_files,varargin{:});
+    [opt_par_values,hessian_mat,gg,fval,invhess] = newrat(objective_function,start_par_value,bounds,analytic_grad,crit,nit,0,Verbose, Save_files,varargin{:});
     %hessian_mat is the plain outer product gradient Hessian
   case 6
     [opt_par_values, hessian_mat, Scale, fval] = gmhmaxlik(objective_function, start_par_value, ...
diff --git a/matlab/optimization/mr_gstep.m b/matlab/optimization/mr_gstep.m
index 51bfb09c4..a2335e1b8 100644
--- a/matlab/optimization/mr_gstep.m
+++ b/matlab/optimization/mr_gstep.m
@@ -1,4 +1,4 @@
-function [f0, x, ig] = mr_gstep(h1,x,func0,htol0,Verbose,Save_files,varargin)
+function [f0, x, ig] = mr_gstep(h1,x,bounds,func0,htol0,Verbose,Save_files,varargin)
 % function [f0, x, ig] = mr_gstep(h1,x,func0,htol0,varargin)
 %
 % Gibbs type step in optimisation
@@ -39,6 +39,9 @@ if isempty(htol0)
 else
     htol = htol0;
 end
+if length(htol)==1,
+    htol=htol*ones(n,1);
+end
 f0=feval(func0,x,varargin{:});
 
 xh1=x;
@@ -58,8 +61,8 @@ while i<n
     xh1(i)=x(i)-h1(i);
     fx = feval(func0,xh1,varargin{:});
     f_1(:,i)=fx;
-    if hcheck && htol<1
-        htol=min(1,max(min(abs(dx))*2,htol*10));
+    if hcheck && htol(i)<1
+        htol(i)=min(1,max(min(abs(dx))*2,htol(i)*10));
         h1(i)=h10;
         xh1(i)=x(i);
         i=i-1;
@@ -68,7 +71,7 @@ while i<n
         hh=gg;
         gg(i)=(f1(i)'-f_1(i)')./(2.*h1(i));
         hh(i) = 1/max(1.e-9,abs( (f1(i)+f_1(i)-2*f0)./(h1(i)*h1(i)) ));
-        if gg(i)*(hh(i)*gg(i))/2 > htol
+        if gg(i)*(hh(i)*gg(i))/2 > htol(i)
             [f0 x fc retcode] = csminit1(func0,x,f0,gg,0,diag(hh),Verbose,varargin{:});
             ig(i)=1;
             if Verbose
@@ -77,6 +80,7 @@ while i<n
         end
         xh1=x;
     end
+    x = check_bounds(x,bounds);
     if Save_files
         save gstep.mat x h1 f0
     end
@@ -85,3 +89,19 @@ if Save_files
     save gstep.mat x h1 f0
 end
 
+return
+
+
+function x = check_bounds(x,bounds)
+
+inx = find(x>=bounds(:,2));
+if ~isempty(inx),
+    x(inx) = bounds(inx,2)-eps;
+end
+
+inx = find(x<=bounds(:,1));
+if ~isempty(inx),
+    x(inx) = bounds(inx,1)+eps;
+end
+
+
diff --git a/matlab/optimization/mr_hessian.m b/matlab/optimization/mr_hessian.m
index 109c0147c..040472437 100644
--- a/matlab/optimization/mr_hessian.m
+++ b/matlab/optimization/mr_hessian.m
@@ -86,8 +86,10 @@ if outer_product_gradient
 end
 
 i=0;
+hhtol=htol*ones(n,1);
 while i<n
     i=i+1;
+    htol=hhtol(i);
     h10=h1(i);
     hcheck=0;
     xh1(i)=x(i)+h1(i);
@@ -164,7 +166,8 @@ while i<n
     if hcheck && htol<1
         htol=min(1,max(min(abs(dx))*2,htol*10));
         h1(i)=h10;
-        i=0;
+        hhtol(i) = htol;
+        i=i-1;
     end
 end
 
@@ -263,4 +266,4 @@ else
     hh1 = [];
 end
 
-htol1=htol;
+htol1=hhtol;
diff --git a/matlab/optimization/newrat.m b/matlab/optimization/newrat.m
index 44c7b35b5..51afa8391 100644
--- a/matlab/optimization/newrat.m
+++ b/matlab/optimization/newrat.m
@@ -1,4 +1,4 @@
-function [xparam1, hh, gg, fval, igg] = newrat(func0, x, analytic_derivation, ftol0, nit, flagg, Verbose, Save_files, varargin)
+function [xparam1, hh, gg, fval, igg] = newrat(func0, x, bounds, analytic_derivation, ftol0, nit, flagg, Verbose, Save_files, varargin)
 %  [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit, flagg, varargin)
 %
 %  Optimiser with outer product gradient and with sequences of univariate steps
@@ -86,8 +86,11 @@ if isempty(hh)
             igg=inv(hh);
         end
     end
-    if htol0>htol
-        htol=htol0;
+    if max(htol0)>htol
+        skipline()
+        disp_verbose('Numerical noise in the likelihood')
+        disp_verbose('Tolerance has to be relaxed')
+        skipline()
     end
 else
     hh0=hh;
@@ -147,7 +150,9 @@ while norm(gg)>gtol && check==0 && jit<nit
         iggx(find(ig),find(ig)) = inv( hhx(find(ig),find(ig)) );
         [fvala,x0,fc,retcode] = csminit1(func0,x0,fval,ggx,0,iggx,Verbose,varargin{:});
     end
-    [fvala, x0, ig] = mr_gstep(h1,x0,func0,htol,Verbose,Save_files,varargin{:});
+    x0 = check_bounds(x0,bounds);
+    [fvala, x0, ig] = mr_gstep(h1,x0,bounds,func0,htol0,Verbose,Save_files,varargin{:});
+    x0 = check_bounds(x0,bounds);
     nig=[nig ig];
     disp_verbose('Sequence of univariate steps!!',Verbose)
     fval=fvala;
@@ -155,6 +160,7 @@ while norm(gg)>gtol && check==0 && jit<nit
         disp_verbose('Try diagonal Hessian',Verbose)
         ihh=diag(1./(diag(hhg)));
         [fval2,x0,fc,retcode2] = csminit1(func0,x0,fval,gg,0,ihh,Verbose,varargin{:});
+        x0 = check_bounds(x0,bounds);
         if (fval-fval2)>=ftol
             disp_verbose('Diagonal Hessian successful',Verbose)
         end
@@ -164,6 +170,7 @@ while norm(gg)>gtol && check==0 && jit<nit
         disp_verbose('Try gradient direction',Verbose)
         ihh0=inx.*1.e-4;
         [fval3,x0,fc,retcode3] = csminit1(func0,x0,fval,gg,0,ihh0,Verbose,varargin{:});
+        x0 = check_bounds(x0,bounds);
         if (fval-fval3)>=ftol
             disp_verbose('Gradient direction successful',Verbose)
         end
@@ -199,7 +206,7 @@ while norm(gg)>gtol && check==0 && jit<nit
         disp_verbose(['FVAL          ',num2str(fval)],Verbose)
         disp_verbose(['Improvement   ',num2str(fval0(icount)-fval)],Verbose)
         disp_verbose(['Ftol          ',num2str(ftol)],Verbose)
-        disp_verbose(['Htol          ',num2str(htol0)],Verbose)
+        disp_verbose(['Htol          ',num2str(max(htol0))],Verbose)
         disp_verbose(['Gradient norm  ',num2str(norm(gg))],Verbose)
         ee=eig(hh);
         disp_verbose(['Minimum Hessian eigenvalue ',num2str(min(ee))],Verbose)
@@ -211,7 +218,7 @@ while norm(gg)>gtol && check==0 && jit<nit
         disp_verbose(['FVAL          ',num2str(fval)],Verbose)
         disp_verbose(['Improvement   ',num2str(df)],Verbose)
         disp_verbose(['Ftol          ',num2str(ftol)],Verbose)
-        disp_verbose(['Htol          ',num2str(htol0)],Verbose)
+        disp_verbose(['Htol          ',num2str(max(htol0))],Verbose)
         htol=htol_base;
         if norm(x(:,icount)-xparam1)>1.e-12 && analytic_derivation==0,
             try
@@ -227,8 +234,7 @@ while norm(gg)>gtol && check==0 && jit<nit
             if isempty(dum),
                 outer_product_gradient=0;
             end
-            if htol0>htol
-                htol=htol0;
+            if max(htol0)>htol
                 skipline()
                 disp_verbose('Numerical noise in the likelihood',Verbose)
                 disp_verbose('Tolerance has to be relaxed',Verbose)
@@ -297,3 +303,16 @@ if check==1,
 end
 
 return
+
+
+function x = check_bounds(x,bounds)
+
+inx = find(x>=bounds(:,2));
+if ~isempty(inx),
+    x(inx) = bounds(inx,2)-eps;
+end
+
+inx = find(x<=bounds(:,1));
+if ~isempty(inx),
+    x(inx) = bounds(inx,1)+eps;
+end