diff --git a/src/dbuffer.hpp b/src/dbuffer.hpp
index 573177b1..9a24dbf1 100644
--- a/src/dbuffer.hpp
+++ b/src/dbuffer.hpp
@@ -111,7 +111,7 @@ namespace zmq
             return has_msg;
         }
 
-        inline bool probe (bool (*fn)(msg_t &))
+        inline bool probe (bool (*fn)(const msg_t &))
         {
             scoped_lock_t lock (sync);
             return (*fn) (*front);
diff --git a/src/msg.cpp b/src/msg.cpp
index dfc3239f..906443cf 100644
--- a/src/msg.cpp
+++ b/src/msg.cpp
@@ -267,7 +267,7 @@ bool zmq::msg_t::is_identity () const
     return (u.base.flags & identity) == identity;
 }
 
-bool zmq::msg_t::is_delimiter ()
+bool zmq::msg_t::is_delimiter () const
 {
     return u.base.type == type_delimiter;
 }
diff --git a/src/msg.hpp b/src/msg.hpp
index 4516588e..7a47fff9 100644
--- a/src/msg.hpp
+++ b/src/msg.hpp
@@ -70,7 +70,7 @@ namespace zmq
         int64_t fd ();
         void set_fd (int64_t fd_);
         bool is_identity () const;
-        bool is_delimiter ();
+        bool is_delimiter () const;
         bool is_vsm ();
         bool is_cmsg ();
 
diff --git a/src/pipe.cpp b/src/pipe.cpp
index 38127b79..4c485a0b 100644
--- a/src/pipe.cpp
+++ b/src/pipe.cpp
@@ -406,7 +406,7 @@ void zmq::pipe_t::terminate (bool delay_)
     }
 }
 
-bool zmq::pipe_t::is_delimiter (msg_t &msg_)
+bool zmq::pipe_t::is_delimiter (const msg_t &msg_)
 {
     return msg_.is_delimiter ();
 }
diff --git a/src/pipe.hpp b/src/pipe.hpp
index a031bbc3..c9a2cade 100644
--- a/src/pipe.hpp
+++ b/src/pipe.hpp
@@ -199,7 +199,7 @@ namespace zmq
         blob_t identity;
 
         //  Returns true if the message is delimiter; false otherwise.
-        static bool is_delimiter (msg_t &msg_);
+        static bool is_delimiter (const msg_t &msg_);
 
         //  Computes appropriate low watermark from the given high watermark.
         static int compute_lwm (int hwm_);
diff --git a/src/ypipe.hpp b/src/ypipe.hpp
index e142e69a..c580ce24 100644
--- a/src/ypipe.hpp
+++ b/src/ypipe.hpp
@@ -166,7 +166,7 @@ namespace zmq
         //  Applies the function fn to the first elemenent in the pipe
         //  and returns the value returned by the fn.
         //  The pipe mustn't be empty or the function crashes.
-        inline bool probe (bool (*fn)(T &))
+        inline bool probe (bool (*fn)(const T &))
         {
                 bool rc = check_read ();
                 zmq_assert (rc);
diff --git a/src/ypipe_base.hpp b/src/ypipe_base.hpp
index a711778e..a3d67656 100644
--- a/src/ypipe_base.hpp
+++ b/src/ypipe_base.hpp
@@ -37,7 +37,7 @@ namespace zmq
         virtual bool flush () = 0;
         virtual bool check_read () = 0;
         virtual bool read (T *value_) = 0;
-        virtual bool probe (bool (*fn)(T &)) = 0;
+        virtual bool probe (bool (*fn)(const T &)) = 0;
     };
 }
 
diff --git a/src/ypipe_conflate.hpp b/src/ypipe_conflate.hpp
index 99a267dc..31d0f3d5 100644
--- a/src/ypipe_conflate.hpp
+++ b/src/ypipe_conflate.hpp
@@ -107,7 +107,7 @@ namespace zmq
         //  Applies the function fn to the first elemenent in the pipe
         //  and returns the value returned by the fn.
         //  The pipe mustn't be empty or the function crashes.
-        inline bool probe (bool (*fn)(T &))
+        inline bool probe (bool (*fn)(const T &))
         {
             return dbuffer.probe (fn);
         }