diff --git a/gdb/ChangeLog b/gdb/ChangeLog
index 59db3402186..3cf2cf10bf9 100644
--- a/gdb/ChangeLog
+++ b/gdb/ChangeLog
@@ -1,3 +1,11 @@
+2020-07-10  Pedro Alves  <pedro@palves.net>
+
+	* frame-tailcall.c (dwarf2_tailcall_sniffer_first): Only swallow
+	NO_ENTRY_VALUE_ERROR / MEMORY_ERROR / OPTIMIZED_OUT_ERROR /
+	NOT_AVAILABLE_ERROR.
+	* value.c (value_optimized_out): Only swallow MEMORY_ERROR /
+	OPTIMIZED_OUT_ERROR / NOT_AVAILABLE_ERROR.
+
 2020-07-10  Simon Marchi  <simon.marchi@polymtl.ca>
 	    Pedro Alves  <pedro@palves.net>
 
diff --git a/gdb/dwarf2/frame-tailcall.c b/gdb/dwarf2/frame-tailcall.c
index 2d219f13f9d..7ea6daca25b 100644
--- a/gdb/dwarf2/frame-tailcall.c
+++ b/gdb/dwarf2/frame-tailcall.c
@@ -377,7 +377,6 @@ dwarf2_tailcall_sniffer_first (struct frame_info *this_frame,
      get_frame_address_in_block will decrease it by 1 in such case.  */
   this_pc = get_frame_address_in_block (this_frame);
 
-  /* Catch any unwinding errors.  */
   try
     {
       int sp_regnum;
@@ -404,7 +403,22 @@ dwarf2_tailcall_sniffer_first (struct frame_info *this_frame,
     {
       if (entry_values_debug)
 	exception_print (gdb_stdout, except);
-      return;
+
+      switch (except.error)
+	{
+	case NO_ENTRY_VALUE_ERROR:
+	  /* Thrown by call_site_find_chain.  */
+	case MEMORY_ERROR:
+	case OPTIMIZED_OUT_ERROR:
+	case NOT_AVAILABLE_ERROR:
+	  /* These can normally happen when we try to access an
+	     optimized out or unavailable register, either in a
+	     physical register or spilled to memory.  */
+	  return;
+	}
+
+      /* Let unexpected errors propagate.  */
+      throw;
     }
 
   /* Ambiguous unwind or unambiguous unwind verified as matching.  */
diff --git a/gdb/value.c b/gdb/value.c
index 97a099ddbd3..00d8ded2ae0 100644
--- a/gdb/value.c
+++ b/gdb/value.c
@@ -1412,7 +1412,18 @@ value_optimized_out (struct value *value)
 	}
       catch (const gdb_exception_error &ex)
 	{
-	  /* Fall back to checking value->optimized_out.  */
+	  switch (ex.error)
+	    {
+	    case MEMORY_ERROR:
+	    case OPTIMIZED_OUT_ERROR:
+	    case NOT_AVAILABLE_ERROR:
+	      /* These can normally happen when we try to access an
+		 optimized out or unavailable register, either in a
+		 physical register or spilled to memory.  */
+	      break;
+	    default:
+	      throw;
+	    }
 	}
     }