diff --git a/NEWS b/NEWS
index 645bbf5..1231937 100644
--- a/NEWS
+++ b/NEWS
@@ -16,6 +16,10 @@
   - new leak check heuristic 'length64' to detect interior pointers
     pointing at offset 64bit of a block, when the first 8 bytes contains
     the block size - 8. This is e.g. used by sqlite3MemMalloc.
+  - if a syscall param (e.g. bind struct sockaddr, sendmsg struct msghdr,
+    ...) has several fields not initialised, an error is now reported for
+    each field. Previously, an error was reported only for the first wrong
+    field.
 
 * Helgrind:
   - Race condition error message with allocated blocks also show
diff --git a/coregrind/m_errormgr.c b/coregrind/m_errormgr.c
index e7de4eb..3143d78 100644
--- a/coregrind/m_errormgr.c
+++ b/coregrind/m_errormgr.c
@@ -677,7 +677,8 @@
    All detected errors are notified here; this routine decides if/when the
    user should see the error. */
 void VG_(maybe_record_error) ( ThreadId tid, 
-                               ErrorKind ekind, Addr a, const HChar* s, void* extra )
+                               ErrorKind ekind, Addr a, 
+                               const HChar* s, void* extra )
 {
           Error  err;
           Error* p;
@@ -818,9 +819,17 @@
          break;
    }
 
+   /* copy the error string, if there is one.
+      note: if we would have many errors with big strings, using a
+      DedupPoolAlloc for these strings will avoid duplicating
+      such string in each error using it. */
+   if (NULL != p->string) {
+      p->string = VG_(arena_strdup)(VG_AR_CORE, "errormgr.mre.2", p->string);
+   }
+
    /* copy block pointed to by 'extra', if there is one */
    if (NULL != p->extra && 0 != extra_size) { 
-      void* new_extra = VG_(malloc)("errormgr.mre.2", extra_size);
+      void* new_extra = VG_(malloc)("errormgr.mre.3", extra_size);
       VG_(memcpy)(new_extra, p->extra, extra_size);
       p->extra = new_extra;
    }
@@ -870,7 +879,7 @@
       Then update the 'extra' part with VG_(tdict).tool_update_extra),
       because that can have an affect on whether it's suppressed.  Ignore
       the size return value of VG_(tdict).tool_update_extra, because we're
-      not copying 'extra'. */
+      not copying 'extra'. Similarly, 's' is also not copied. */
    (void)VG_TDICT_CALL(tool_update_extra, &err);
 
    su = is_suppressible_error(&err);
@@ -1514,10 +1523,11 @@
       // n_expanded >= n_ips_expanded.
 
       Int* n_offsets_per_ip;
-      // n_offsets_per_ip[i] gives the nr of offsets in fun_offsets and obj_offsets
-      // resulting of the expansion of ips[i].
+      // n_offsets_per_ip[i] gives the nr of offsets in fun_offsets and
+      // obj_offsets resulting of the expansion of ips[i].
       // The sum of all n_expanded_per_ip must be equal to n_expanded.
-      // This array allows to retrieve the position in ips corresponding to an ixInput.
+      // This array allows to retrieve the position in ips corresponding to 
+      // an ixInput.
 
       // size (in elements) of fun_offsets and obj_offsets.
       // (fun|obj)_offsets are reallocated if more space is needed
@@ -1570,9 +1580,10 @@
 }
 
 /* free the memory in ip2fo.
-   At debuglog 4, su (or NULL) will be used to show the matching (or non matching)
-   with ip2fo. */
-static void clearIPtoFunOrObjCompleter ( Supp  *su, IPtoFunOrObjCompleter* ip2fo)
+   At debuglog 4, su (or NULL) will be used to show the matching
+   (or non matching) with ip2fo. */
+static void clearIPtoFunOrObjCompleter ( Supp  *su, 
+                                         IPtoFunOrObjCompleter* ip2fo)
 {
    if (DEBUG_ERRORMGR || VG_(debugLog_getLevel)() >= 4) {
       if (su)
@@ -1672,7 +1683,8 @@
               i++) {
             ip2fo->obj_offsets[i] = ip2fo->names_free;
             if (DEBUG_ERRORMGR) 
-               VG_(printf) ("   set obj_offset %lu to %d\n", i, ip2fo->names_free);
+               VG_(printf) ("   set obj_offset %lu to %d\n", 
+                            i, ip2fo->names_free);
          }
       }
       ip2fo->names_free += VG_(strlen)(caller_name) + 1;
diff --git a/coregrind/m_syswrap/syswrap-generic.c b/coregrind/m_syswrap/syswrap-generic.c
index 39ee199..35a2b40 100644
--- a/coregrind/m_syswrap/syswrap-generic.c
+++ b/coregrind/m_syswrap/syswrap-generic.c
@@ -1074,8 +1074,13 @@
 #endif
 
       default:
-         VG_(sprintf) ( outmsg, description, "" );
-         PRE_MEM_READ( outmsg, (Addr) sa, salen );
+         /* No specific information about this address family.
+            Let's just check the full data following the family.
+            Note that this can give false positive if this (unknown)
+            struct sockaddr_???? has padding bytes between its elements. */
+         VG_(sprintf) ( outmsg, description, "sa_data" );
+         PRE_MEM_READ( outmsg, (Addr)&sa->sa_family + sizeof(sa->sa_family),
+                       salen );
          break;
    }
    
diff --git a/include/pub_tool_errormgr.h b/include/pub_tool_errormgr.h
index 26339ab..3ec673c 100644
--- a/include/pub_tool_errormgr.h
+++ b/include/pub_tool_errormgr.h
@@ -66,9 +66,15 @@
    seen before.  If it has, the existing error record will have its count
    incremented.
 
-   'tid' can be found as for VG_(record_ExeContext)().  The `extra' field can
-   be stack-allocated;  it will be copied by the core if needed (but it
-   won't be copied if it's NULL).
+   'tid' can be found as for VG_(record_ExeContext)().  The `s' string
+   and `extra' field can be stack-allocated;  they will be copied by the core
+   if needed (but it won't be copied if it's NULL).
+   Note that `ekind' and `s' are also used to generate a suppression.
+   `s' should therefore not contain data depending on the specific
+   execution (such as addresses, values) but should rather contain
+   e.g. a system call parameter symbolic name.
+   `extra' is also (optionally) used for generating a suppression
+   (see pub_tool_tooliface.h print_extra_suppression_info).
 
    If no 'a', 's' or 'extra' of interest needs to be recorded, just use
    NULL for them.  */
diff --git a/memcheck/tests/linux/rfcomm.c b/memcheck/tests/linux/rfcomm.c
index 02dcd7e..dbda1f5 100644
--- a/memcheck/tests/linux/rfcomm.c
+++ b/memcheck/tests/linux/rfcomm.c
@@ -3,6 +3,7 @@
 #include <stdlib.h>
 #include <sys/types.h>
 #include <sys/socket.h>
+#include "../../memcheck.h"
 
 /* user space headers might not be there, define things ourselves. */
 typedef struct {
@@ -34,20 +35,39 @@
     }
 
   struct vui_sockaddr_rc aAddr;
+
+  // Store correct values in aAddr but marking it undefined
+  // so as to generate errors. We need to have deterministic
+  // undefined values to have a reproducible test.
+  aAddr.rc_family = VUI_AF_BLUETOOTH;
+  aAddr.rc_bdaddr = *VUI_BDADDR_ANY;
+  aAddr.rc_channel = 5;
+  VALGRIND_MAKE_MEM_UNDEFINED(&aAddr, sizeof(aAddr));
+  // We re-assign below each piece one by one, so as to
+  // have the piece marked initialised.
+
+
   // Ignore return values.
 
-  // Missing family
+  // Everything uninit (family, ...)
+  bind(nSocket, (struct sockaddr *) &aAddr, sizeof(aAddr));
+
+  // Same but with an unknown family (we hope :)
+  aAddr.rc_family = 12345;
+  // (reset everything to uninit)
+  VALGRIND_MAKE_MEM_UNDEFINED(&aAddr, sizeof(aAddr));
   bind(nSocket, (struct sockaddr *) &aAddr, sizeof(aAddr));
 
   aAddr.rc_family = VUI_AF_BLUETOOTH;
-  // Missing bdaddr.
+  // uninit bdaddr and channel.
   bind(nSocket, (struct sockaddr *) &aAddr, sizeof(aAddr));
 
   aAddr.rc_bdaddr = *VUI_BDADDR_ANY;
-  // Missing channel.
+  // uninit channel.
   bind(nSocket, (struct sockaddr *) &aAddr, sizeof(aAddr));
 
   aAddr.rc_channel = 5;
+  // Everything correctly init.
   bind(nSocket, (struct sockaddr *) &aAddr, sizeof(aAddr));
 
   return 0;
diff --git a/memcheck/tests/linux/rfcomm.stderr.exp b/memcheck/tests/linux/rfcomm.stderr.exp
index 293ae2b..0c16048 100644
--- a/memcheck/tests/linux/rfcomm.stderr.exp
+++ b/memcheck/tests/linux/rfcomm.stderr.exp
@@ -1,24 +1,64 @@
 Syscall param socketcall.bind(my_addr.sa_family) points to uninitialised byte(s)
    ...
-   by 0x........: main (rfcomm.c:40)
+   by 0x........: main (rfcomm.c:53)
  Address 0x........ is on thread 1's stack
- in frame #1, created by main (rfcomm.c:25)
- Uninitialised value was created by a stack allocation
-   at 0x........: main (rfcomm.c:25)
+ in frame #1, created by main (rfcomm.c:26)
+ Uninitialised value was created by a client request
+   at 0x........: main (rfcomm.c:45)
 
 Syscall param socketcall.bind(my_addr.rc_bdaddr) points to uninitialised byte(s)
    ...
-   by 0x........: main (rfcomm.c:44)
+   by 0x........: main (rfcomm.c:53)
  Address 0x........ is on thread 1's stack
- in frame #1, created by main (rfcomm.c:25)
- Uninitialised value was created by a stack allocation
-   at 0x........: main (rfcomm.c:25)
+ in frame #1, created by main (rfcomm.c:26)
+ Uninitialised value was created by a client request
+   at 0x........: main (rfcomm.c:45)
 
 Syscall param socketcall.bind(my_addr.rc_channel) points to uninitialised byte(s)
    ...
-   by 0x........: main (rfcomm.c:48)
+   by 0x........: main (rfcomm.c:53)
  Address 0x........ is on thread 1's stack
- in frame #1, created by main (rfcomm.c:25)
- Uninitialised value was created by a stack allocation
-   at 0x........: main (rfcomm.c:25)
+ in frame #1, created by main (rfcomm.c:26)
+ Uninitialised value was created by a client request
+   at 0x........: main (rfcomm.c:45)
+
+Syscall param socketcall.bind(my_addr.sa_family) points to uninitialised byte(s)
+   ...
+   by 0x........: main (rfcomm.c:59)
+ Address 0x........ is on thread 1's stack
+ in frame #1, created by main (rfcomm.c:26)
+ Uninitialised value was created by a client request
+   at 0x........: main (rfcomm.c:58)
+
+Syscall param socketcall.bind(my_addr.sa_data) points to uninitialised byte(s)
+   ...
+   by 0x........: main (rfcomm.c:59)
+ Address 0x........ is on thread 1's stack
+ in frame #1, created by main (rfcomm.c:26)
+ Uninitialised value was created by a client request
+   at 0x........: main (rfcomm.c:58)
+
+Syscall param socketcall.bind(my_addr.rc_bdaddr) points to uninitialised byte(s)
+   ...
+   by 0x........: main (rfcomm.c:63)
+ Address 0x........ is on thread 1's stack
+ in frame #1, created by main (rfcomm.c:26)
+ Uninitialised value was created by a client request
+   at 0x........: main (rfcomm.c:58)
+
+Syscall param socketcall.bind(my_addr.rc_channel) points to uninitialised byte(s)
+   ...
+   by 0x........: main (rfcomm.c:63)
+ Address 0x........ is on thread 1's stack
+ in frame #1, created by main (rfcomm.c:26)
+ Uninitialised value was created by a client request
+   at 0x........: main (rfcomm.c:58)
+
+Syscall param socketcall.bind(my_addr.rc_channel) points to uninitialised byte(s)
+   ...
+   by 0x........: main (rfcomm.c:67)
+ Address 0x........ is on thread 1's stack
+ in frame #1, created by main (rfcomm.c:26)
+ Uninitialised value was created by a client request
+   at 0x........: main (rfcomm.c:58)