diff --git a/lldb/source/Breakpoint/BreakpointResolverAddress.cpp b/lldb/source/Breakpoint/BreakpointResolverAddress.cpp
--- a/lldb/source/Breakpoint/BreakpointResolverAddress.cpp
+++ b/lldb/source/Breakpoint/BreakpointResolverAddress.cpp
@@ -121,16 +121,27 @@
 
   if (filter.AddressPasses(m_addr)) {
     if (breakpoint.GetNumLocations() == 0) {
-      // If the address is just an offset, and we're given a module, see if we
-      // can find the appropriate module loaded in the binary, and fix up
-      // m_addr to use that.
-      if (!m_addr.IsSectionOffset() && m_module_filespec) {
+      // If the address is just an offset ...
+      if (!m_addr.IsSectionOffset()) {
+        ModuleSP containing_module_sp = nullptr;
         Target &target = breakpoint.GetTarget();
-        ModuleSpec module_spec(m_module_filespec);
-        ModuleSP module_sp = target.GetImages().FindFirstModule(module_spec);
-        if (module_sp) {
+        if (m_module_filespec) {
+          // ... and we're given a module, see if we can find the
+          // appropriate module loaded in the binary, and fix up
+          // m_addr to use that.
+          ModuleSpec module_spec(m_module_filespec);
+          containing_module_sp =
+              target.GetImages().FindFirstModule(module_spec);
+        } else {
+          // ... and we're not given a module, see if the offset is
+          // somewhere in the executable module. If it is, then we'll
+          // fix up m_addr to use that.
+          containing_module_sp = target.GetExecutableModule();
+        }
+        if (containing_module_sp) {
           Address tmp_address;
-          if (module_sp->ResolveFileAddress(m_addr.GetOffset(), tmp_address))
+          if (containing_module_sp->ResolveFileAddress(m_addr.GetOffset(),
+                                                       tmp_address))
             m_addr = tmp_address;
         }
       }
diff --git a/lldb/source/Commands/Options.td b/lldb/source/Commands/Options.td
--- a/lldb/source/Commands/Options.td
+++ b/lldb/source/Commands/Options.td
@@ -128,13 +128,15 @@
     Arg<"AddressOrExpression">, Required,
     Desc<"Set the breakpoint at the specified address.  If the address maps "
     "uniquely to a particular binary, then the address will be converted to "
-    "a \"file\"address, so that the breakpoint will track that binary+offset "
+    "a \"file\" address, so that the breakpoint will track that binary+offset "
     "no matter where the binary eventually loads.  Alternately, if you also "
     "specify the module - with the -s option - then the address will be "
     "treated as a file address in that module, and resolved accordingly.  "
     "Again, this will allow lldb to track that offset on subsequent reloads.  "
     "The module need not have been loaded at the time you specify this "
-    "breakpoint, and will get resolved when the module is loaded.">;
+    "breakpoint, and will get resolved when the module is loaded.  If no "
+    "module is specified, the binary being debugged is considered as a "
+    "fallback.">;
   def breakpoint_set_name : Option<"name", "n">, Group<3>, Arg<"FunctionName">,
     Completion<"Symbol">, Required,
     Desc<"Set the breakpoint by function name.  Can be repeated multiple times "
diff --git a/lldb/test/API/commands/breakpoint/set/address-nomodule/Makefile b/lldb/test/API/commands/breakpoint/set/address-nomodule/Makefile
new file mode 100644
--- /dev/null
+++ b/lldb/test/API/commands/breakpoint/set/address-nomodule/Makefile
@@ -0,0 +1,3 @@
+C_SOURCES := inferior.c
+
+include Makefile.rules
diff --git a/lldb/test/API/commands/breakpoint/set/address-nomodule/TestBreakpointAddressNoModule.py b/lldb/test/API/commands/breakpoint/set/address-nomodule/TestBreakpointAddressNoModule.py
new file mode 100644
--- /dev/null
+++ b/lldb/test/API/commands/breakpoint/set/address-nomodule/TestBreakpointAddressNoModule.py
@@ -0,0 +1,36 @@
+import lldb
+from lldbsuite.test.decorators import *
+from lldbsuite.test.lldbtest import *
+from lldbsuite.test import lldbutil
+
+class TestCase(TestBase):
+
+    mydir = TestBase.compute_mydir(__file__)
+
+    def get_address_from_symbol(self, symbol):
+        target = lldbutil.run_to_breakpoint_make_target(self, "a.out", True)
+        bp = target.BreakpointCreateByName(symbol, None)
+        address = bp.GetLocationAtIndex(0).GetAddress().GetFileAddress()
+        return address
+
+    def test_set_address_no_module(self):
+        self.build()
+
+        main_address = self.get_address_from_symbol("main")
+
+        tgt = lldbutil.run_to_breakpoint_make_target(self)
+        dbg = tgt.GetDebugger()
+
+        dbg.HandleCommand(f"break set -a {main_address:#x}")
+        self.assertTrue(tgt.GetNumBreakpoints() == 1)
+
+        bp = tgt.GetBreakpointAtIndex(0)
+        self.assertTrue(bp != None)
+
+        _, _, thread, _ = lldbutil.run_to_breakpoint_do_run(self, tgt, bp)
+        self.assertTrue(thread.GetNumFrames() >= 1)
+
+        thread_pc = thread.GetFrameAtIndex(0).GetPCAddress()
+        self.assertTrue(thread_pc != None)
+
+        self.assertTrue(main_address==thread_pc.GetFileAddress())
diff --git a/lldb/test/API/commands/breakpoint/set/address-nomodule/inferior.c b/lldb/test/API/commands/breakpoint/set/address-nomodule/inferior.c
new file mode 100644
--- /dev/null
+++ b/lldb/test/API/commands/breakpoint/set/address-nomodule/inferior.c
@@ -0,0 +1,6 @@
+int function(int a) { return a; }
+
+int main() {
+  int f = function(10);
+  return f;
+}