diff --git a/internal/governor/conn.go b/internal/governor/conn.go
index 864cff6..fd00f13 100644
--- a/internal/governor/conn.go
+++ b/internal/governor/conn.go
@@ -211,6 +211,10 @@ func readSockstat(environ []string) updateData {
 			res.GroupLeader = sockstat.GetBool(parts[1])
 		case "is_importing":
 			res.IsImporting = sockstat.BoolValue(parts[1])
+		case "import_skip_push_limit":
+			res.ImportSkipPushLimit = sockstat.BoolValue(parts[1])
+		case "import_soft_throttling":
+			res.ImportSoftThrottling = sockstat.BoolValue(parts[1])
 		}
 	}
 
diff --git a/internal/governor/governor.go b/internal/governor/governor.go
index 5354b87..7c3db1d 100644
--- a/internal/governor/governor.go
+++ b/internal/governor/governor.go
@@ -76,6 +76,12 @@ type updateData struct {
 	CommandID string `json:"command_id,omitempty"`
 	// IsImporting is true if the command is an import.
 	IsImporting bool `json:"is_importing,omitempty"`
+	// ImportSkipPushLimit is true if the command is an import and
+	// we want to skip the push limit for a command.
+	ImportSkipPushLimit bool `json:"import_skip_push_limit,omitempty"`
+	// ImportSoftThrottling is true if the command is an import and
+	// we want to apply it some soft throttling policies.
+	ImportSoftThrottling bool `json:"import_soft_throttling,omitempty"`
 }
 
 func update(w io.Writer, ud updateData) error {
diff --git a/internal/integration/integration_test.go b/internal/integration/integration_test.go
index e8024f0..0f53156 100644
--- a/internal/integration/integration_test.go
+++ b/internal/integration/integration_test.go
@@ -211,6 +211,40 @@ func (suite *SpokesReceivePackTestSuite) TestBadDateAllowedWithOverride() {
 	assert.Contains(suite.T(), string(out), " badDate:", "should still complain about a bad date")
 }
 
+func (suite *SpokesReceivePackTestSuite) TestSpokesReceivePackAllowedWhenWithIsImportingSockStat() {
+	assert.NoError(suite.T(), chdir(suite.T(), suite.remoteRepo), "unable to chdir into our remote Git repo")
+	// Set a really low value to receive.maxsize in order to make it fail
+	require.NoError(suite.T(), exec.Command("git", "config", "receive.maxsize", "1").Run())
+
+	assert.NoError(suite.T(), chdir(suite.T(), suite.localRepo), "unable to chdir into our local Git repo")
+	cmd := exec.Command("git", "push", "--all", "--receive-pack=spokes-receive-pack-wrapper", "r")
+	cmd.Env = append(os.Environ(),
+		"GIT_SOCKSTAT_VAR_is_importing=bool:true",
+	)
+	err := cmd.Run()
+	assert.NoError(
+		suite.T(),
+		err,
+		"unexpected failure with the custom spokes-receive-pack program; it should have succeeded")
+}
+
+func (suite *SpokesReceivePackTestSuite) TestSpokesReceivePackAllowedWhenWithImportSkipPushLimitSockStat() {
+	assert.NoError(suite.T(), chdir(suite.T(), suite.remoteRepo), "unable to chdir into our remote Git repo")
+	// Set a really low value to receive.maxsize in order to make it fail
+	require.NoError(suite.T(), exec.Command("git", "config", "receive.maxsize", "1").Run())
+
+	assert.NoError(suite.T(), chdir(suite.T(), suite.localRepo), "unable to chdir into our local Git repo")
+	cmd := exec.Command("git", "push", "--all", "--receive-pack=spokes-receive-pack-wrapper", "r")
+	cmd.Env = append(os.Environ(),
+		"GIT_SOCKSTAT_VAR_import_skip_push_limit=bool:true",
+	)
+	err := cmd.Run()
+	assert.NoError(
+		suite.T(),
+		err,
+		"unexpected failure with the custom spokes-receive-pack program; it should have succeeded")
+}
+
 func (suite *SpokesReceivePackTestSuite) TestWithGovernor() {
 	started := make(chan any)
 	govSock, msgs, cleanup := startFakeGovernor(suite.T(), started, nil)
diff --git a/internal/spokes/spokes.go b/internal/spokes/spokes.go
index e4254f2..e651256 100644
--- a/internal/spokes/spokes.go
+++ b/internal/spokes/spokes.go
@@ -955,7 +955,11 @@ func (r *spokesReceivePack) isFsckConfigEnabled() bool {
 }
 
 func (r *spokesReceivePack) getMaxInputSize() (int, error) {
-	if isImporting() {
+	// We want to skip the default push limit when the `import_skip_push_limit`
+	// stat is set only.
+	// We keep using the `is_import` here for backward compatibility only,
+	// which should be removed on a subsequent PR.
+	if isImporting() || skipPushLimit() {
 		return 80 * 1024 * 1024 * 1024, nil /* 80 GB */
 	}
 
@@ -1234,6 +1238,10 @@ func isImporting() bool {
 	return sockstat.GetBool("is_importing")
 }
 
+func skipPushLimit() bool {
+	return sockstat.GetBool("import_skip_push_limit")
+}
+
 func allowBadDate() bool {
 	return isImporting() && sockstat.GetBool("allow_baddate_in_import")
 }