diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2025-02-13-12-31-53.gh-issue-115802.0kN4xM.rst b/Misc/NEWS.d/next/Core_and_Builtins/2025-02-13-12-31-53.gh-issue-115802.0kN4xM.rst
new file mode 100644
index 00000000000000..b645c6b9e1cf20
--- /dev/null
+++ b/Misc/NEWS.d/next/Core_and_Builtins/2025-02-13-12-31-53.gh-issue-115802.0kN4xM.rst
@@ -0,0 +1,2 @@
+Use the more efficient "medium" code model for JIT-compiled code on
+supported platforms.
diff --git a/Tools/jit/_stencils.py b/Tools/jit/_stencils.py
index 8b6957f8bdbdfc..4ddbe967438bd1 100644
--- a/Tools/jit/_stencils.py
+++ b/Tools/jit/_stencils.py
@@ -84,9 +84,8 @@ class HoleValue(enum.Enum):
     "R_AARCH64_MOVW_UABS_G3": "patch_aarch64_16d",
     # x86_64-unknown-linux-gnu:
     "R_X86_64_64": "patch_64",
-    "R_X86_64_GOTPCREL": "patch_32r",
     "R_X86_64_GOTPCRELX": "patch_x86_64_32rx",
-    "R_X86_64_PC32": "patch_32r",
+    "R_X86_64_PLT32": "patch_32r",
     "R_X86_64_REX_GOTPCRELX": "patch_x86_64_32rx",
     # x86_64-apple-darwin:
     "X86_64_RELOC_BRANCH": "patch_32r",
@@ -226,11 +225,11 @@ def remove_jump(self, *, alignment: int = 1) -> None:
                 offset -= 3
             case Hole(
                 offset=offset,
-                kind="IMAGE_REL_I386_REL32" | "X86_64_RELOC_BRANCH",
+                kind="IMAGE_REL_I386_REL32" | "R_X86_64_PLT32" | "X86_64_RELOC_BRANCH",
                 value=HoleValue.CONTINUE,
                 symbol=None,
-                addend=-4,
-            ) as hole:
+                addend=addend,
+            ) as hole if _signed(addend) == -4:
                 # jmp 5
                 jump = b"\xE9\x00\x00\x00\x00"
                 offset -= 1
@@ -243,17 +242,6 @@ def remove_jump(self, *, alignment: int = 1) -> None:
             ) as hole:
                 # b #4
                 jump = b"\x00\x00\x00\x14"
-            case Hole(
-                offset=offset,
-                kind="R_X86_64_GOTPCRELX",
-                value=HoleValue.GOT,
-                symbol="_JIT_CONTINUE",
-                addend=addend,
-            ) as hole:
-                assert _signed(addend) == -4
-                # jmp qword ptr [rip]
-                jump = b"\xFF\x25\x00\x00\x00\x00"
-                offset -= 2
             case _:
                 return
         if self.body[offset:] == jump and offset % alignment == 0:
diff --git a/Tools/jit/_targets.py b/Tools/jit/_targets.py
index 7eb433e2a5b207..84fa1a6ed25a18 100644
--- a/Tools/jit/_targets.py
+++ b/Tools/jit/_targets.py
@@ -522,7 +522,7 @@ def get_target(host: str) -> _COFF | _ELF | _MachO:
         args = ["-fms-runtime-lib=dll"]
         target = _COFF(host, args=args)
     elif re.fullmatch(r"x86_64-.*-linux-gnu", host):
-        args = ["-fpic"]
+        args = ["-fno-pic", "-mcmodel=medium", "-mlarge-data-threshold=0"]
         target = _ELF(host, args=args)
     else:
         raise ValueError(host)