diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index 872550018f3f..cd96fb92c084 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -45,7 +45,7 @@
 import matplotlib as mpl
 from matplotlib import (
     _api, backend_tools as tools, cbook, colors, docstring, textpath,
-    tight_bbox, transforms, widgets, get_backend, is_interactive, rcParams)
+    transforms, widgets, get_backend, is_interactive, rcParams)
 from matplotlib._pylab_helpers import Gcf
 from matplotlib.backend_managers import ToolManager
 from matplotlib.cbook import _setattr_cm
@@ -2273,11 +2273,7 @@ def print_figure(
                 if not cbook._str_equal(color, "auto"):
                     stack.enter_context(self.figure._cm_set(**{prop: color}))
 
-            if bbox_inches is None:
-                bbox_inches = rcParams['savefig.bbox']
-
-            if (self.figure.get_constrained_layout() or
-                    bbox_inches == "tight"):
+            if self.figure.get_constrained_layout():
                 # we need to trigger a draw before printing to make sure
                 # CL works.  "tight" also needs a draw to get the right
                 # locations:
@@ -2289,22 +2285,6 @@ def print_figure(
                 with getattr(renderer, "_draw_disabled", nullcontext)():
                     self.figure.draw(renderer)
 
-            if bbox_inches:
-                if bbox_inches == "tight":
-                    bbox_inches = self.figure.get_tightbbox(
-                        renderer, bbox_extra_artists=bbox_extra_artists)
-                    if pad_inches is None:
-                        pad_inches = rcParams['savefig.pad_inches']
-                    bbox_inches = bbox_inches.padded(pad_inches)
-
-                # call adjust_bbox to save only the given area
-                restore_bbox = tight_bbox.adjust_bbox(self.figure, bbox_inches,
-                                                      canvas.fixed_dpi)
-
-                _bbox_inches_restore = (bbox_inches, restore_bbox)
-            else:
-                _bbox_inches_restore = None
-
             # we have already done CL above, so turn it off:
             stack.enter_context(self.figure._cm_set(constrained_layout=False))
             try:
@@ -2316,12 +2296,19 @@ def print_figure(
                         facecolor=facecolor,
                         edgecolor=edgecolor,
                         orientation=orientation,
-                        bbox_inches_restore=_bbox_inches_restore,
                         **kwargs)
+                    if bbox_inches is None:
+                        bbox_inches = rcParams["savefig.bbox"]
+                    if bbox_inches == "tight":
+                        bbox_inches = self.figure.get_tightbbox(
+                            self.figure._cachedRenderer,
+                            bbox_extra_artists=bbox_extra_artists)
+                        if pad_inches is None:
+                            pad_inches = rcParams["savefig.pad_inches"]
+                        bbox_inches = bbox_inches.padded(pad_inches)
+                    if bbox_inches:
+                        canvas.adjust_bbox(filename, bbox_inches)
             finally:
-                if bbox_inches and restore_bbox:
-                    restore_bbox()
-
                 self.figure.set_canvas(self)
             return result
 
diff --git a/lib/matplotlib/backends/backend_agg.py b/lib/matplotlib/backends/backend_agg.py
index 74f1d911b561..ad34e8e7e4c9 100644
--- a/lib/matplotlib/backends/backend_agg.py
+++ b/lib/matplotlib/backends/backend_agg.py
@@ -562,6 +562,13 @@ def print_tif(self, filename_or_obj, *, pil_kwargs=None):
 
     print_tiff = print_tif
 
+    def adjust_bbox(self, filename, bbox_inches):
+        bbox = self.figure.dpi_scale_trans.transform_bbox(bbox_inches)
+        h = self.figure.bbox.height
+        img = Image.open(filename)
+        img = img.crop((bbox.x0, h - bbox.y1, bbox.x1, h - bbox.y0))
+        img.save(filename, format=img.format)  # TODO: also copy metadata
+
 
 @_Backend.export
 class _BackendAgg(_Backend):
diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
index 2eb6f090db26..bdf0974e8536 100644
--- a/lib/matplotlib/backends/backend_pdf.py
+++ b/lib/matplotlib/backends/backend_pdf.py
@@ -2719,6 +2719,32 @@ def draw(self):
         self.figure.draw_no_output()
         return super().draw()
 
+    def adjust_bbox(self, filename, bbox_inches):
+        bbox = self.figure.dpi_scale_trans.transform_bbox(bbox_inches)
+        # What about PdfPages?
+        with open(filename, "a+b") as file:
+            file.seek(0)
+            buf = file.read()
+            page_pos = file.tell()
+            pageid = self.figure._cachedRenderer.file.pageList[-1].id
+            page_match = re.search(
+                rb"(?s)%d 0 obj\n.*?/MediaBox.*?\nendobj\n" % pageid, buf)
+            file.write(re.sub(br"/MediaBox \[[^]]*\]", b"/MediaBox %s"
+                              % pdfRepr(bbox.extents.tolist()), page_match[0]))
+            startxref_pos = file.tell()
+            file.write(b"xref\n")
+            file.write(b"0 1\n0000000000 65535 f \n")
+            file.write(b"%d 1\n%010d 00000 n \n" % (pageid, page_pos))
+            file.write(b"trailer\n")
+            trailer_match = re.search(
+                rb"(?s)trailer\n<< (.*) >>\nstartxref\n(\d+)\n%%EOF",
+                buf[buf.rfind(b"trailer\n"):])
+            file.write(
+                b"<< %s /Prev %s >>\n" % (trailer_match[1], trailer_match[2]))
+            file.write(b"startxref\n")
+            file.write(b"%d\n" % startxref_pos)
+            file.write(b"%%EOF\n")
+
 
 FigureManagerPdf = FigureManagerBase
 
diff --git a/lib/matplotlib/backends/backend_svg.py b/lib/matplotlib/backends/backend_svg.py
index a1a11061b978..cbd156f7fdea 100644
--- a/lib/matplotlib/backends/backend_svg.py
+++ b/lib/matplotlib/backends/backend_svg.py
@@ -6,6 +6,7 @@
 import itertools
 import logging
 import os
+import pathlib
 import re
 import uuid
 
@@ -1345,6 +1346,17 @@ def draw(self):
         self.figure.draw_no_output()
         return super().draw()
 
+    def adjust_bbox(self, filename, bbox_inches):
+        bbox = self.figure.dpi_scale_trans.transform_bbox(bbox_inches)
+        buf = pathlib.Path(filename).read_text()
+        w, h, x, y = map(short_float_fmt, [
+            bbox.width, bbox.height,
+            bbox.x0, self.figure.bbox.height - bbox.y1])
+        buf = re.sub('width="[^"]*"', f'width="{w}pt"', buf, 1)
+        buf = re.sub('height="[^"]*"', f'height="{h}pt"', buf, 1)
+        buf = re.sub('viewBox="[^"]*"', f'viewBox="{x} {y} {w} {h}"', buf, 1)
+        pathlib.Path(filename).write_text(buf)
+
 
 FigureManagerSVG = FigureManagerBase