diff --git a/src/ext/oxli/counting.hh b/src/ext/oxli/counting.hh
index 779755b..cbfe220 100644
--- a/src/ext/oxli/counting.hh
+++ b/src/ext/oxli/counting.hh
@@ -140,7 +140,7 @@ public:
 
     // Writing to the tables outside of defined methods has undefined behavior!
     // As such, this should only be used to return read-only interfaces
-    Byte ** get_raw_tables()
+    Byte ** get_raw_tables() const
     {
         return _counts;
     }
diff --git a/src/kernel.cc b/src/kernel.cc
index 74fe953..01e9dc1 100644
--- a/src/kernel.cc
+++ b/src/kernel.cc
@@ -44,7 +44,7 @@ Kernel::
 
 float
 Kernel::
-kernel(khmer::CountingHash &a, khmer::CountingHash &b)
+kernel(const khmer::CountingHash &a, const khmer::CountingHash &b)
 {
     _check_hash_dimensions(a, b);
     return 0.0;
@@ -228,7 +228,7 @@ _get_hash(std::string &filename)
 
 void
 Kernel::
-_check_hash_dimensions(khmer::CountingHash &a, khmer::CountingHash &b)
+_check_hash_dimensions(const khmer::CountingHash &a, const khmer::CountingHash &b)
 {
     size_t i;
     bool ok = true;
diff --git a/src/kernel.hh b/src/kernel.hh
index 56096ee..d02755a 100644
--- a/src/kernel.hh
+++ b/src/kernel.hh
@@ -62,8 +62,8 @@ protected:
     // Ensure `a` and `b` have the same counting hash dimensions. Throws an
     // exception if they are not.
     virtual void
-    _check_hash_dimensions     (khmer::CountingHash        &a,
-                                khmer::CountingHash        &b);
+    _check_hash_dimensions     (const khmer::CountingHash        &a,
+                                const khmer::CountingHash        &b);
     CountingHashShrPtr
     _get_hash                  (std::string                &filename);
 
@@ -81,8 +81,8 @@ public:
 
     // Calculate the kernel between two counting hashes
     virtual float
-    kernel                      (khmer::CountingHash   &a,
-                                 khmer::CountingHash   &b);
+    kernel                      (const khmer::CountingHash   &a,
+                                 const khmer::CountingHash   &b);
 
     // Calculate the kernel between all pairs of counting hashes in parallel
     virtual void
diff --git a/src/kernels/ip.cc b/src/kernels/ip.cc
index e7f5c84..5b910a1 100644
--- a/src/kernels/ip.cc
+++ b/src/kernels/ip.cc
@@ -23,7 +23,7 @@ namespace metrics
 {
 
 float
-IPKernel::kernel(khmer::CountingHash &a, khmer::CountingHash &b)
+IPKernel::kernel(const khmer::CountingHash &a, const khmer::CountingHash &b)
 {
     std::vector<float> tab_scores;
     khmer::Byte **a_counts = a.get_raw_tables();
diff --git a/src/kernels/ip.hh b/src/kernels/ip.hh
index e29f5b3..94cf3ab 100644
--- a/src/kernels/ip.hh
+++ b/src/kernels/ip.hh
@@ -29,8 +29,8 @@ namespace metrics
 class IPKernel : public Kernel
 {
 public:
-    float kernel               (khmer::CountingHash        &a,
-                                khmer::CountingHash        &b);
+    float kernel               (const khmer::CountingHash        &a,
+                                const khmer::CountingHash        &b);
 };
 
 }} // end namespace kwip::metrics
diff --git a/src/kernels/wip.cc b/src/kernels/wip.cc
index d34235e..0b4983a 100644
--- a/src/kernels/wip.cc
+++ b/src/kernels/wip.cc
@@ -38,7 +38,7 @@ add_hashtable(const std::string &hash_fname)
         uint64_t tab_count = 0;
         // Save these here to avoid dereferencing twice below.
         uint16_t *this_popcount = _pop_counts[tab];
-        khmer::Byte *this_count = counts[tab];
+        const khmer::Byte *this_count = counts[tab];
         for (size_t j = 0; j < _tablesizes[tab]; j++) {
             if (this_count[j] > 0) {
                 __sync_fetch_and_add(&(this_popcount[j]), 1);
@@ -117,18 +117,18 @@ calculate_pairwise(std::vector<std::string> &hash_fnames)
 
 float
 WIPKernel::
-kernel(khmer::CountingHash &a, khmer::CountingHash &b)
+kernel(const khmer::CountingHash &a, const khmer::CountingHash &b)
 {
     std::vector<float>          tab_kernels;
-    khmer::Byte               **a_counts = a.get_raw_tables();
-    khmer::Byte               **b_counts = b.get_raw_tables();
+    khmer::Byte         **a_counts = a.get_raw_tables();
+    khmer::Byte         **b_counts = b.get_raw_tables();
 
     _check_hash_dimensions(a, b);
 
     for (size_t tab = 0; tab < _n_tables; tab++) {
         double tab_kernel = 0.0;
-        khmer::Byte *A = a_counts[tab];
-        khmer::Byte *B = b_counts[tab];
+        const khmer::Byte *A = a_counts[tab];
+        const khmer::Byte *B = b_counts[tab];
         for (size_t bin = 0; bin < _tablesizes[tab]; bin++) {
             float bin_entropy = _bin_entropies[tab][bin];
             tab_kernel += A[bin] * B[bin] * bin_entropy;
diff --git a/src/kernels/wip.hh b/src/kernels/wip.hh
index 8044213..5194725 100644
--- a/src/kernels/wip.hh
+++ b/src/kernels/wip.hh
@@ -38,8 +38,8 @@ public:
     add_hashtable               (const std::string     &hash_fname);
 
     float
-    kernel                      (khmer::CountingHash   &a,
-                                 khmer::CountingHash   &b);
+    kernel                      (const khmer::CountingHash   &a,
+                                 const khmer::CountingHash   &b);
 
     void
     calculate_pairwise          (std::vector<std::string> &hash_fnames);