diff --git a/A_opt.py b/A_opt.py
index a96b3ab2..f9f191c2 100644
--- a/A_opt.py
+++ b/A_opt.py
@@ -659,20 +659,25 @@ def G( x, y, alpha=1., beta=0., trans='N'):
     # h vector.
     h = matrix( 0., (K*(K+1)/2 + K*(K+1)*(K+1), 1))
     # F := Fisher matrix
-    if nsofar is not None or di2 is not None:
-        if nsofar is None:
-            F = matrix( 0., (K, K))
-            F[::K+1] = di2
-        else:
-            F = Fisher_matrix( si2, nsofar, di2)
+    if nsofar is None:
+        F = matrix( 0., (K, K))
     else:
-        F = None
+        F = Fisher_matrix( si2, nsofar, di2)
+    if di2 is not None: F[::K+1] = di2
+    elif np.all( np.diag( si2) == 0):
+        # If the diagonal elements of 1/s[i,i]^2 are all zero, the Fisher
+        # information matrix is singular, and the quantities are determined
+        # up to a constant.  In this case, we constrain the
+        # mean of the quantities.  This corresponds to adding a constant
+        # omega to the Fisher matrix.  The optimal allocation does not 
+        # depend on the value of omega.
+        omega = 1.
+        F += omega
 
     row = K*(K+1)/2
     for i in xrange(K):
-        if F is not None:
-            for j in xrange(K):
-                h[row + j*(K+1) : row + (j+1)*(K+1)-1] = F[:,j]
+        for j in xrange(K):
+            h[row + j*(K+1) : row + (j+1)*(K+1)-1] = F[:,j]
         h[row + (i+1)*(K+1)-1] = 1.  # e_i^t
         h[row + K*(K+1) + i] = 1.    # e_i
         row += (K+1)*(K+1)
@@ -1151,12 +1156,22 @@ def test_sumdR2( ntrials=10, tol=1e-9):
     print 'Timing for aligned sum dR: %f seconds per call.' % (tfast/ntrials)
     return success
 
+def test_relative_only():
+    K = 5
+    np.random.seed( 1)
+    sij = matrix( np.random.rand( K*K), (K,K))
+    sij = 0.5*(sij + sij.T)
+    for i in range(K): sij[i,i] = np.inf
+    nij = A_optimize_fast( sij)
+    print nij
+
 def unit_test():
     test_Gfunc( ntrials=100)
     test_kkt_solver( ntrials=100)
     test_sumdR2()
     
 if __name__ == '__main__':
+    test_relative_only()
     K = 200
     sij = matrix( np.random.rand( K*K), (K, K))
     nsofar = matrix( 0.2*np.random.rand( K*K), (K, K))
diff --git a/test_diffnet.py b/test_diffnet.py
index a4ef488a..afdd82db 100644
--- a/test_diffnet.py
+++ b/test_diffnet.py
@@ -11,12 +11,16 @@ def check_optimality( sij, nij, optimality='A', delta=1E-1, ntimes=10):
     '''
     K = sij.size[0]
     C = covariance( cvxopt.div( nij, sij**2))
-    fC = dict(
-        A = np.trace( C), 
-        D = np.log( linalg.det( C)),
-        E = np.max( linalg.eig( C)[0]).real,
-        Etree = np.max( linalg.eig( C)[0]).real
-    )
+    fC = dict()
+    if optimality=='A':
+        fC['A'] = np.trace( C) 
+    if optimality=='D':
+        fC['D'] = np.log( linalg.det( C))
+    if optimality=='E':
+        fC['E'] = np.max( linalg.eig( C)[0]).real
+    if optimality=='Etree':
+        fC['Etree'] = np.max( linalg.eig( C)[0]).real
+    
     df = np.zeros( ntimes)
     for t in xrange( ntimes):
         zeta = matrix( 1. + 2*delta*(np.random.rand(  K, K) - 0.5))
@@ -149,6 +153,20 @@ def check_sparse_A_optimal( sij, ntimes=10, delta=1e-1, tol=1e-5):
 
     return success and success2
 
+def check_relative_only_A_optimal( sij):
+    '''
+    '''
+    sij = matrix(sij)
+    K = sij.size[0]
+    for i in range(K): sij[i,i] = np.inf
+    nij = A_optimize( sij)
+    success = check_optimality( sij, nij)
+    if (not success):
+        print 'FAIL: A_optimize for relative-only measurements did not generate optimal.'
+    else:
+        print 'SUCCESS: A_optimize for relative-only measurements.'
+    return success
+    
 def check_hessian( dF, d2F, x0):
     '''
     Check the Hessian for correctness.
@@ -268,7 +286,6 @@ def unitTest( tol=1.e-4):
                         [ 0.1, 1., 0.1 ],
                         [ 0.1, 0.1, 1.2 ]])
 
-
     from scipy.optimize import check_grad
 
     def F( x):
@@ -336,6 +353,10 @@ def d2F( x):
     if (check_sparse_A_optimal( sij)):
         print 'Sparse A-optimal passed!'
 
+    # Check A-optimal when only relative measurements are included.
+    if (check_relative_only_A_optimal( sij)):
+        print 'Relative-only A-optimal passed!'
+
     # Test covariance computation
     if (test_covariance(5, T=4000)):
         print 'Covariance computation passed!'