diff --git a/mesonbuild/compilers/c.py b/mesonbuild/compilers/c.py
index a59b7d384..1c9b9b4fa 100644
--- a/mesonbuild/compilers/c.py
+++ b/mesonbuild/compilers/c.py
@@ -780,9 +780,12 @@ class CCompiler(Compiler):
             args = ['-l' + libname]
             if self.links(code, env, extra_args=args):
                 return args
+        # Ensure that we won't modify the list that was passed to us
+        extra_dirs = extra_dirs[:]
+        # Search in the system libraries too
+        extra_dirs += self.get_library_dirs()
         # Not found or we want to use a specific libtype? Try to find the
         # library file itself.
-        extra_dirs += self.get_library_dirs()
         prefixes, suffixes = self.get_library_naming(env, libtype)
         # Triply-nested loop!
         for d in extra_dirs:
diff --git a/mesonbuild/dependencies/base.py b/mesonbuild/dependencies/base.py
index 66bc3b470..fefab3f3f 100644
--- a/mesonbuild/dependencies/base.py
+++ b/mesonbuild/dependencies/base.py
@@ -516,6 +516,7 @@ class PkgConfigDependency(ExternalDependency):
                                       (self.name, out))
         self.link_args = []
         libpaths = []
+        static_libs_notfound = []
         for lib in self._convert_mingw_paths(shlex.split(out)):
             # If we want to use only static libraries, we have to look for the
             # file ourselves instead of depending on the compiler to find it
@@ -524,13 +525,26 @@ class PkgConfigDependency(ExternalDependency):
             if self.static:
                 if lib.startswith('-L'):
                     libpaths.append(lib[2:])
+                    print(lib)
                     continue
+                # FIXME: try to handle .la files in static mode too?
                 elif lib.startswith('-l') and libpaths:
                     args = self.compiler.find_library(lib[2:], self.env, libpaths, libtype='static')
                     if not args or len(args) < 1:
-                        raise DependencyException('Static library not found for {!r}'
-                                                  ''.format(lib[2:]))
-                    lib = args[0]
+                        if lib in static_libs_notfound:
+                            continue
+                        mlog.warning('Static library {!r} not found for dependency {!r}, may '
+                                     'not be statically linked'.format(lib[2:], self.name))
+                        static_libs_notfound.append(lib)
+                        # Preserve the -l arg since we couldn't resolve it to
+                        # a static library. Also need all previous -L args now.
+                        for p in libpaths:
+                            lp = '-L' + p
+                            if lp not in self.link_args:
+                                self.link_args.append(lp)
+                    else:
+                        # Replace -l arg with full path to static library
+                        lib = args[0]
             elif lib.endswith(".la"):
                 shared_libname = self.extract_libtool_shlib(lib)
                 shared_lib = os.path.join(os.path.dirname(lib), shared_libname)
diff --git a/run_unittests.py b/run_unittests.py
index ac627da9c..fd424bee7 100755
--- a/run_unittests.py
+++ b/run_unittests.py
@@ -1567,9 +1567,13 @@ int main(int argc, char **argv) {
 
     def test_pkgconfig_static(self):
         '''
-        Test that the we only use static libraries when `static: true` is
+        Test that the we prefer static libraries when `static: true` is
         passed to dependency() with pkg-config. Can't be an ordinary test
         because we need to build libs and try to find them from meson.build
+
+        Also test that it's not a hard error to have unsatisfiable library deps
+        since system libraries -lm will never be found statically.
+        https://github.com/mesonbuild/meson/issues/2785
         '''
         if not shutil.which('pkg-config'):
             raise unittest.SkipTest('pkg-config not found')
diff --git a/test cases/frameworks/7 gnome/meson.build b/test cases/frameworks/7 gnome/meson.build
index bb9d09f36..795f458e9 100644
--- a/test cases/frameworks/7 gnome/meson.build	
+++ b/test cases/frameworks/7 gnome/meson.build	
@@ -30,6 +30,9 @@ gobj = dependency('gobject-2.0')
 gir = dependency('gobject-introspection-1.0')
 gmod = dependency('gmodule-2.0')
 
+# Test that static deps don't error out when static libraries aren't found
+glib_static = dependency('glib-2.0', static : true)
+
 subdir('resources-data')
 subdir('resources')
 subdir('gir')
diff --git a/test cases/unit/17 pkgconfig static/foo.pc.in b/test cases/unit/17 pkgconfig static/foo.pc.in
index 94d803154..b26c0b0a2 100644
--- a/test cases/unit/17 pkgconfig static/foo.pc.in	
+++ b/test cases/unit/17 pkgconfig static/foo.pc.in	
@@ -7,4 +7,5 @@ Name: libfoo
 Description: A foo library.
 Version: 1.0
 Libs: -L${libdir} -lfoo
+Libs.private: -lm
 Cflags: -I${includedir}