diff --git a/include/armadillo_bits/arma_forward.hpp b/include/armadillo_bits/arma_forward.hpp
index 1bad37f4..b35d64ef 100644
--- a/include/armadillo_bits/arma_forward.hpp
+++ b/include/armadillo_bits/arma_forward.hpp
@@ -129,6 +129,17 @@ class spop_htrans;
 class spop_vectorise_row;
 class spop_vectorise_col;
 
+class spop_rel_lt_pre;
+class spop_rel_lt_post;
+class spop_rel_gt_pre;
+class spop_rel_gt_post;
+class spop_rel_lteq_pre;
+class spop_rel_lteq_post;
+class spop_rel_gteq_pre;
+class spop_rel_gteq_post;
+class spop_rel_eq;
+class spop_rel_noteq;
+
 class spglue_plus;
 class spglue_minus;
 class spglue_schur;
diff --git a/include/armadillo_bits/fn_accu.hpp b/include/armadillo_bits/fn_accu.hpp
index 821649c1..f775a7bb 100644
--- a/include/armadillo_bits/fn_accu.hpp
+++ b/include/armadillo_bits/fn_accu.hpp
@@ -1111,18 +1111,15 @@ accu(const SpOp<T1, spop_type>& expr)
 
 
 
-// optimisations for sparse relational operations
-
-
-template<typename T1>
+template<typename T1, typename spop_type>
 arma_warn_unused
 inline
 uword
-accu(const mtSpOp<uword,T1,spop_rel_lt_pre>& X)
+accu(const mtSpOp<uword,T1,spop_type>& X, const typename arma_spop_rel_only<spop_type>::result* junk1 = nullptr, const typename arma_not_cx<typename T1::elem_type>::result* junk2 = nullptr)
   {
   arma_debug_sigprint();
-  
-  // operation: accu(scalar < spmat)
+  arma_ignore(junk1);
+  arma_ignore(junk2);
   
   typedef typename T1::elem_type eT;
   
@@ -1132,29 +1129,70 @@ accu(const mtSpOp<uword,T1,spop_rel_lt_pre>& X)
   
   const uword n_zeros = P.get_n_elem() - P.get_n_nonzero();
   
+  const eT zero = eT(0);
+  
+  // shortcuts
+  
+  if( (is_same_type<spop_type, spop_rel_eq   >::yes) && (k == zero) )  { return n_zeros;           }
+  if( (is_same_type<spop_type, spop_rel_noteq>::yes) && (k == zero) )  { return P.get_n_nonzero(); }
+  
   // take into account all implicit zeros
-  uword count = (k < eT(0)) ? n_zeros : 0;
+  
+  bool use_n_zeros;
+  
+       if(is_same_type<spop_type, spop_rel_eq       >::yes)  { use_n_zeros = (zero == k   ); }
+  else if(is_same_type<spop_type, spop_rel_noteq    >::yes)  { use_n_zeros = (zero != k   ); }
+  else if(is_same_type<spop_type, spop_rel_lt_pre   >::yes)  { use_n_zeros = (k    <  zero); }
+  else if(is_same_type<spop_type, spop_rel_lt_post  >::yes)  { use_n_zeros = (zero <  k   ); }
+  else if(is_same_type<spop_type, spop_rel_gt_pre   >::yes)  { use_n_zeros = (k    >  zero); }
+  else if(is_same_type<spop_type, spop_rel_gt_post  >::yes)  { use_n_zeros = (zero >  k   ); }
+  else if(is_same_type<spop_type, spop_rel_lteq_pre >::yes)  { use_n_zeros = (k    <= zero); }
+  else if(is_same_type<spop_type, spop_rel_lteq_post>::yes)  { use_n_zeros = (zero <= k   ); }
+  else if(is_same_type<spop_type, spop_rel_gteq_pre >::yes)  { use_n_zeros = (k    >= zero); }
+  else if(is_same_type<spop_type, spop_rel_gteq_post>::yes)  { use_n_zeros = (zero >= k   ); }
+  else { use_n_zeros = false; }
+  
+  uword count = (use_n_zeros) ? n_zeros : 0;
   
   typename SpProxy<T1>::const_iterator_type it     = P.begin();
   typename SpProxy<T1>::const_iterator_type it_end = P.end();
   
   // take into account all non-zero elements
-  for(; it != it_end; ++it)  { count += (k < (*it)) ? uword(1) : uword(0); }
+  for(; it != it_end; ++it)
+    {
+    const eT val = (*it);
+    
+    bool condition;
+    
+         if(is_same_type<spop_type, spop_rel_eq       >::yes)  { condition = (val == k  ); }
+    else if(is_same_type<spop_type, spop_rel_noteq    >::yes)  { condition = (val != k  ); }
+    else if(is_same_type<spop_type, spop_rel_lt_pre   >::yes)  { condition = (k   <  val); }
+    else if(is_same_type<spop_type, spop_rel_lt_post  >::yes)  { condition = (val <  k  ); }
+    else if(is_same_type<spop_type, spop_rel_gt_pre   >::yes)  { condition = (k   >  val); }
+    else if(is_same_type<spop_type, spop_rel_gt_post  >::yes)  { condition = (val >  k  ); }
+    else if(is_same_type<spop_type, spop_rel_lteq_pre >::yes)  { condition = (k   <= val); }
+    else if(is_same_type<spop_type, spop_rel_lteq_post>::yes)  { condition = (val <= k  ); }
+    else if(is_same_type<spop_type, spop_rel_gteq_pre >::yes)  { condition = (k   >= val); }
+    else if(is_same_type<spop_type, spop_rel_gteq_post>::yes)  { condition = (val >= k  ); }
+    else { condition = false; }
+    
+    count += (condition) ? uword(1) : uword(0);
+    }
   
   return count;
   }
 
 
 
-template<typename T1>
+template<typename T1, typename spop_type>
 arma_warn_unused
 inline
 uword
-accu(const mtSpOp<uword,T1,spop_rel_gt_pre>& X)
+accu(const mtSpOp<uword,T1,spop_type>& X, const typename arma_spop_rel_only<spop_type>::result* junk1 = nullptr, const typename arma_cx_only<typename T1::elem_type>::result* junk2 = nullptr)
   {
   arma_debug_sigprint();
-  
-  // operation: accu(scalar > spmat)
+  arma_ignore(junk1);
+  arma_ignore(junk2);
   
   typedef typename T1::elem_type eT;
   
@@ -1164,270 +1202,39 @@ accu(const mtSpOp<uword,T1,spop_rel_gt_pre>& X)
   
   const uword n_zeros = P.get_n_elem() - P.get_n_nonzero();
   
+  const eT zero = eT(0);
+  
+  // shortcuts
+  
+  if( (is_same_type<spop_type, spop_rel_eq   >::yes) && (k == zero) )  { return n_zeros;           }
+  if( (is_same_type<spop_type, spop_rel_noteq>::yes) && (k == zero) )  { return P.get_n_nonzero(); }
+  
   // take into account all implicit zeros
-  uword count = (k > eT(0)) ? n_zeros : 0;
+  
+  bool use_n_zeros;
+  
+       if(is_same_type<spop_type, spop_rel_eq   >::yes)  { use_n_zeros = (zero == k); }
+  else if(is_same_type<spop_type, spop_rel_noteq>::yes)  { use_n_zeros = (zero != k); }
+  else { use_n_zeros = false; }
+  
+  uword count = (use_n_zeros) ? n_zeros : 0;
   
   typename SpProxy<T1>::const_iterator_type it     = P.begin();
   typename SpProxy<T1>::const_iterator_type it_end = P.end();
   
   // take into account all non-zero elements
-  for(; it != it_end; ++it)  { count += (k > (*it)) ? uword(1) : uword(0); }
-  
-  return count;
-  }
-
-
-
-template<typename T1>
-arma_warn_unused
-inline
-uword
-accu(const mtSpOp<uword,T1,spop_rel_lteq_pre>& X)
-  {
-  arma_debug_sigprint();
-  
-  // operation: accu(scalar <= spmat)
-  
-  typedef typename T1::elem_type eT;
-  
-  const eT k = X.aux;
-  
-  const SpProxy<T1> P(X.m);
-  
-  const uword n_zeros = P.get_n_elem() - P.get_n_nonzero();
-  
-  // take into account all implicit zeros
-  uword count = (k <= eT(0)) ? n_zeros : 0;
-  
-  typename SpProxy<T1>::const_iterator_type it     = P.begin();
-  typename SpProxy<T1>::const_iterator_type it_end = P.end();
-  
-  // take into account all non-zero elements
-  for(; it != it_end; ++it)  { count += (k <= (*it)) ? uword(1) : uword(0); }
-  
-  return count;
-  }
-
-
-
-template<typename T1>
-arma_warn_unused
-inline
-uword
-accu(const mtSpOp<uword,T1,spop_rel_gteq_pre>& X)
-  {
-  arma_debug_sigprint();
-  
-  // operation: accu(scalar >= spmat)
-  
-  typedef typename T1::elem_type eT;
-  
-  const eT k = X.aux;
-  
-  const SpProxy<T1> P(X.m);
-  
-  const uword n_zeros = P.get_n_elem() - P.get_n_nonzero();
-  
-  // take into account all implicit zeros
-  uword count = (k >= eT(0)) ? n_zeros : 0;
-  
-  typename SpProxy<T1>::const_iterator_type it     = P.begin();
-  typename SpProxy<T1>::const_iterator_type it_end = P.end();
-  
-  // take into account all non-zero elements
-  for(; it != it_end; ++it)  { count += (k >= (*it)) ? uword(1) : uword(0); }
-  
-  return count;
-  }
-
-
-
-template<typename T1>
-arma_warn_unused
-inline
-uword
-accu(const mtSpOp<uword,T1,spop_rel_lt_post>& X)
-  {
-  arma_debug_sigprint();
-  
-  // operation: accu(spmat < scalar)
-  
-  typedef typename T1::elem_type eT;
-  
-  const eT k = X.aux;
-  
-  const SpProxy<T1> P(X.m);
-  
-  const uword n_zeros = P.get_n_elem() - P.get_n_nonzero();
-  
-  // take into account all implicit zeros
-  uword count = (eT(0) < k) ? n_zeros : 0;
-  
-  typename SpProxy<T1>::const_iterator_type it     = P.begin();
-  typename SpProxy<T1>::const_iterator_type it_end = P.end();
-  
-  // take into account all non-zero elements
-  for(; it != it_end; ++it)  { count += ((*it) < k) ? uword(1) : uword(0); }
-  
-  return count;
-  }
-
-
-
-template<typename T1>
-arma_warn_unused
-inline
-uword
-accu(const mtSpOp<uword,T1,spop_rel_gt_post>& X)
-  {
-  arma_debug_sigprint();
-  
-  // operation: accu(spmat > scalar)
-  
-  typedef typename T1::elem_type eT;
-  
-  const eT k = X.aux;
-  
-  const SpProxy<T1> P(X.m);
-  
-  const uword n_zeros = P.get_n_elem() - P.get_n_nonzero();
-  
-  // take into account all implicit zeros
-  uword count = (eT(0) > k) ? n_zeros : 0;
-  
-  typename SpProxy<T1>::const_iterator_type it     = P.begin();
-  typename SpProxy<T1>::const_iterator_type it_end = P.end();
-  
-  // take into account all non-zero elements
-  for(; it != it_end; ++it)  { count += ((*it) > k) ? uword(1) : uword(0); }
-  
-  return count;
-  }
-
-
-
-template<typename T1>
-arma_warn_unused
-inline
-uword
-accu(const mtSpOp<uword,T1,spop_rel_lteq_post>& X)
-  {
-  arma_debug_sigprint();
-  
-  // operation: accu(spmat <= scalar)
-  
-  typedef typename T1::elem_type eT;
-  
-  const eT k = X.aux;
-  
-  const SpProxy<T1> P(X.m);
-  
-  const uword n_zeros = P.get_n_elem() - P.get_n_nonzero();
-  
-  // take into account all implicit zeros
-  uword count = (eT(0) <= k) ? n_zeros : 0;
-  
-  typename SpProxy<T1>::const_iterator_type it     = P.begin();
-  typename SpProxy<T1>::const_iterator_type it_end = P.end();
-  
-  // take into account all non-zero elements
-  for(; it != it_end; ++it)  { count += ((*it) <= k) ? uword(1) : uword(0); }
-  
-  return count;
-  }
-
-
-
-template<typename T1>
-arma_warn_unused
-inline
-uword
-accu(const mtSpOp<uword,T1,spop_rel_gteq_post>& X)
-  {
-  arma_debug_sigprint();
-  
-  // operation: accu(spmat >= scalar) ##
-  
-  typedef typename T1::elem_type eT;
-  
-  const eT k = X.aux;
-  
-  const SpProxy<T1> P(X.m);
-  
-  const uword n_zeros = P.get_n_elem() - P.get_n_nonzero();
-  
-  // take into account all implicit zeros
-  uword count = (eT(0) >= k) ? n_zeros : 0;
-  
-  typename SpProxy<T1>::const_iterator_type it     = P.begin();
-  typename SpProxy<T1>::const_iterator_type it_end = P.end();
-  
-  // take into account all non-zero elements
-  for(; it != it_end; ++it)  { count += ((*it) >= k) ? uword(1) : uword(0); }
-  
-  return count;
-  }
-
-
-
-template<typename T1>
-arma_warn_unused
-inline
-uword
-accu(const mtSpOp<uword,T1,spop_rel_eq>& X)
-  {
-  arma_debug_sigprint();
-  
-  // operation: accu(spmat == scalar)
-  
-  typedef typename T1::elem_type eT;
-  
-  const eT k = X.aux;
-  
-  const SpProxy<T1> P(X.m);
-  
-  // accu(spmat == 0) -> number of zeros
-  if(k == eT(0))  { return P.get_n_elem() - P.get_n_nonzero(); }
-  
-  uword count = 0;
-  
-  typename SpProxy<T1>::const_iterator_type it     = P.begin();
-  typename SpProxy<T1>::const_iterator_type it_end = P.end();
-  
-  for(; it != it_end; ++it)  { count += ((*it) == k) ? uword(1) : uword(0); }
-  
-  return count;
-  }
-
-
-
-template<typename T1>
-arma_warn_unused
-inline
-uword
-accu(const mtSpOp<uword,T1,spop_rel_noteq>& X)
-  {
-  arma_debug_sigprint();
-  
-  // operation: accu(spmat != scalar)
-  
-  typedef typename T1::elem_type eT;
-  
-  const eT k = X.aux;
-  
-  const SpProxy<T1> P(X.m);
-  
-  // accu(spmat != 0) -> number of non-zeros
-  if(k == eT(0))  { return P.get_n_nonzero(); }
-  
-  // start with worst-case scenario: all elements are not equal to k
-  uword count = P.get_n_elem();
-  
-  typename SpProxy<T1>::const_iterator_type it     = P.begin();
-  typename SpProxy<T1>::const_iterator_type it_end = P.end();
-  
-  // decrease the count by the number of elements that are equal to k
-  for(; it != it_end; ++it)  { count -= ((*it) == k) ? uword(1) : uword(0); }
+  for(; it != it_end; ++it)
+    {
+    const eT val = (*it);
+    
+    bool condition;
+    
+         if(is_same_type<spop_type, spop_rel_eq   >::yes)  { condition = (val == k); }
+    else if(is_same_type<spop_type, spop_rel_noteq>::yes)  { condition = (val != k); }
+    else { condition = false; }
+    
+    count += (condition) ? uword(1) : uword(0);
+    }
   
   return count;
   }
diff --git a/include/armadillo_bits/restrictors.hpp b/include/armadillo_bits/restrictors.hpp
index 019a5f41..2cb1dabc 100644
--- a/include/armadillo_bits/restrictors.hpp
+++ b/include/armadillo_bits/restrictors.hpp
@@ -182,6 +182,21 @@ template<> struct arma_glue_rel_only< glue_rel_or    > { typedef int result; };
 
 
 
+template<typename T> struct arma_spop_rel_only { };
+
+template<> struct arma_op_rel_only< spop_rel_lt_pre    > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_lt_post   > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_gt_pre    > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_gt_post   > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_lteq_pre  > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_lteq_post > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_gteq_pre  > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_gteq_post > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_eq        > { typedef int result; };
+template<> struct arma_op_rel_only< spop_rel_noteq     > { typedef int result; };
+
+
+
 template<typename T> struct arma_Mat_Col_Row_only { };
 
 template<typename eT> struct arma_Mat_Col_Row_only< Mat<eT> > { typedef Mat<eT> result; };