diff --git a/src/internal/kopia/conn.go b/src/internal/kopia/conn.go
index 315519ab4..b788157f7 100644
--- a/src/internal/kopia/conn.go
+++ b/src/internal/kopia/conn.go
@@ -6,6 +6,8 @@ import (
 
 	"github.com/kopia/kopia/repo"
 	"github.com/kopia/kopia/repo/blob"
+	"github.com/kopia/kopia/repo/compression"
+	"github.com/kopia/kopia/snapshot/policy"
 	"github.com/pkg/errors"
 
 	"github.com/alcionai/corso/internal/common"
@@ -169,3 +171,49 @@ func (w *conn) wrap() error {
 	w.refCount++
 	return nil
 }
+
+// Compression attempts to set the global compression policy for the kopia repo
+// to the given compressor.
+func (w *conn) Compression(ctx context.Context, compressor string) error {
+	comp := compression.Name(compressor)
+
+	if err := checkCompressor(comp); err != nil {
+		return err
+	}
+
+	si := policy.GlobalPolicySourceInfo
+
+	p, err := policy.GetDefinedPolicy(ctx, w.Repository, si)
+	if err != nil {
+		if !errors.Is(err, policy.ErrPolicyNotFound) {
+			return errors.Wrap(err, "getting global compression policy")
+		}
+
+		p = &policy.Policy{}
+	}
+
+	p.CompressionPolicy = policy.CompressionPolicy{
+		CompressorName: compression.Name(comp),
+	}
+
+	err = repo.WriteSession(
+		ctx,
+		w.Repository,
+		repo.WriteSessionOptions{Purpose: "UpdateGlobalCompression"},
+		func(innerCtx context.Context, rw repo.RepositoryWriter) error {
+			return policy.SetPolicy(ctx, rw, si, p)
+		},
+	)
+
+	return errors.Wrap(err, "updating global compression policy")
+}
+
+func checkCompressor(compressor compression.Name) error {
+	for c := range compression.ByName {
+		if c == compressor {
+			return nil
+		}
+	}
+
+	return errors.Errorf("unknown compressor type %s", compressor)
+}
diff --git a/src/internal/kopia/conn_test.go b/src/internal/kopia/conn_test.go
index 7d72153c3..1a83ff6d4 100644
--- a/src/internal/kopia/conn_test.go
+++ b/src/internal/kopia/conn_test.go
@@ -4,6 +4,8 @@ import (
 	"context"
 	"testing"
 
+	"github.com/kopia/kopia/snapshot"
+	"github.com/kopia/kopia/snapshot/policy"
 	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
 	"github.com/stretchr/testify/suite"
@@ -107,3 +109,55 @@ func (suite *WrapperIntegrationSuite) TestOpenAfterClose() {
 	assert.NoError(t, k.Close(ctx))
 	assert.Error(t, k.wrap())
 }
+
+func (suite *WrapperIntegrationSuite) TestBadCompressorType() {
+	ctx := context.Background()
+	t := suite.T()
+
+	k, err := openKopiaRepo(t, ctx)
+	require.NoError(t, err)
+
+	defer func() {
+		assert.NoError(t, k.Close(ctx))
+	}()
+
+	assert.Error(t, k.Compression(ctx, "not-a-compressor"))
+}
+
+func (suite *WrapperIntegrationSuite) TestSetCompressor() {
+	ctx := context.Background()
+	t := suite.T()
+	compressor := "s2-default"
+
+	k, err := openKopiaRepo(t, ctx)
+	require.NoError(t, err)
+
+	defer func() {
+		assert.NoError(t, k.Close(ctx))
+	}()
+
+	assert.NoError(t, k.Compression(ctx, compressor))
+
+	// Check the policy was actually created and has the right compressor.
+	p, err := policy.GetDefinedPolicy(ctx, k.Repository, policy.GlobalPolicySourceInfo)
+	require.NoError(t, err)
+
+	assert.Equal(t, compressor, string(p.CompressionPolicy.CompressorName))
+
+	// Check the global policy will be the effective policy in future snapshots
+	// for some source info.
+	si := snapshot.SourceInfo{
+		Host:     corsoHost,
+		UserName: corsoUser,
+		Path:     "test-path-root",
+	}
+
+	policyTree, err := policy.TreeForSource(ctx, k, si)
+	require.NoError(t, err)
+
+	assert.Equal(
+		t,
+		compressor,
+		string(policyTree.EffectivePolicy().CompressionPolicy.CompressorName),
+	)
+}
diff --git a/src/internal/kopia/wrapper_test.go b/src/internal/kopia/wrapper_test.go
index 0bb867a6c..ba329a938 100644
--- a/src/internal/kopia/wrapper_test.go
+++ b/src/internal/kopia/wrapper_test.go
@@ -486,6 +486,47 @@ func (suite *KopiaIntegrationSuite) TestBackupCollections() {
 	assert.Len(t, rp.Entries, 47)
 }
 
+func (suite *KopiaIntegrationSuite) TestRestoreAfterCompressionChange() {
+	t := suite.T()
+	ctx := context.Background()
+
+	k, err := openKopiaRepo(t, ctx)
+	require.NoError(t, err)
+
+	require.NoError(t, k.Compression(ctx, "s2-default"))
+
+	w := &Wrapper{k}
+
+	tid := uuid.NewString()
+	p1 := []string{tid, "uid", "emails", "fid"}
+	p2 := []string{tid, "uid2", "emails", "fid"}
+	dc1 := mockconnector.NewMockExchangeCollection(p1, 1)
+	dc2 := mockconnector.NewMockExchangeCollection(p2, 1)
+
+	fp1 := append(p1, dc1.Names[0])
+	fp2 := append(p2, dc2.Names[0])
+
+	stats, _, err := w.BackupCollections(ctx, []data.Collection{dc1, dc2})
+	require.NoError(t, err)
+
+	require.NoError(t, k.Compression(ctx, "gzip"))
+
+	expected := map[string][]byte{
+		path.Join(fp1...): dc1.Data[0],
+		path.Join(fp2...): dc2.Data[0],
+	}
+
+	result, err := w.RestoreMultipleItems(
+		ctx,
+		string(stats.SnapshotID),
+		[][]string{fp1, fp2})
+
+	require.NoError(t, err)
+	assert.Equal(t, 2, len(result))
+
+	testForFiles(t, expected, result)
+}
+
 type KopiaSimpleRepoIntegrationSuite struct {
 	suite.Suite
 	w                    *Wrapper