diff --git a/api/queries_org.go b/api/queries_org.go
index 0a6689b35..7366b8bc4 100644
--- a/api/queries_org.go
+++ b/api/queries_org.go
@@ -1,6 +1,7 @@
 package api
 
 import (
+	"fmt"
 	"github.com/cli/cli/v2/internal/ghrepo"
 	"github.com/shurcooL/githubv4"
 )
@@ -47,6 +48,31 @@ type OrgTeam struct {
 	Slug string
 }
 
+// OrganizationTeam fetch the team in an organization with the given slug
+func OrganizationTeam(client *Client, repo ghrepo.Interface, teamSlug string) (*OrgTeam, error) {
+	type responseData struct {
+		Organization struct {
+			Team OrgTeam `graphql:"team(slug: $teamSlug)"`
+		} `graphql:"organization(login: $owner)"`
+	}
+
+	variables := map[string]interface{}{
+		"owner":    githubv4.String(repo.RepoOwner()),
+		"teamSlug": githubv4.String(teamSlug),
+	}
+
+	var query responseData
+	err := client.Query(repo.RepoHost(), "OrganizationTeam", &query, variables)
+	if err != nil {
+		return nil, err
+	}
+	if query.Organization.Team.ID == "" {
+		return nil, fmt.Errorf("could not resolve to a Team with the slug of '%s'", teamSlug)
+	}
+
+	return &query.Organization.Team, nil
+}
+
 // OrganizationTeams fetches all the teams in an organization
 func OrganizationTeams(client *Client, repo ghrepo.Interface) ([]OrgTeam, error) {
 	type responseData struct {
diff --git a/pkg/cmd/project/link/link.go b/pkg/cmd/project/link/link.go
index 39fdfd97e..b2744e90e 100644
--- a/pkg/cmd/project/link/link.go
+++ b/pkg/cmd/project/link/link.go
@@ -80,9 +80,9 @@ func NewCmdLink(f *cmdutil.Factory, runF func(config linkConfig) error) *cobra.C
 			}
 
 			if config.opts.repo != "" && config.opts.team != "" {
-				return fmt.Errorf("specify only one repo or team")
+				return fmt.Errorf("specify only one of `--repo` or `--team`")
 			} else if config.opts.repo == "" && config.opts.team == "" {
-				return fmt.Errorf("specify at least one repo or team")
+				return fmt.Errorf("specify either `--repo` or `--team`")
 			}
 
 			// allow testing of the command without actually running it
@@ -121,50 +121,49 @@ func runLink(config linkConfig) error {
 	c := api.NewClientFromHTTP(httpClient)
 
 	if config.opts.repo != "" {
-		repo, err := api.GitHubRepo(c, ghrepo.New(owner.Login, config.opts.repo))
-		if err != nil {
-			return err
-		}
-		config.opts.repoID = repo.ID
-
-		query, variable := linkRepoArgs(config)
-		err = config.client.Mutate("LinkProjectV2ToRepository", query, variable)
-		if err != nil {
-			return err
-		}
-
-		if config.opts.exporter != nil {
-			return config.opts.exporter.Write(config.io, query.LinkProjectV2ToRepository.Repository)
-		}
-		return printResults(config, query.LinkProjectV2ToRepository.Repository.URL)
-
+		return linkRepo(c, owner, config)
 	} else if config.opts.team != "" {
-		teams, err := api.OrganizationTeams(c, ghrepo.New(owner.Login, ""))
-		if err != nil {
-			return err
-		}
-		for _, team := range teams {
-			if team.Slug == config.opts.team {
-				config.opts.teamID = team.ID
-				break
-			}
-		}
-		if config.opts.teamID == "" {
-			return fmt.Errorf("can't find team %s", config.opts.team)
-		}
-
-		query, variable := linkTeamArgs(config)
-		err = config.client.Mutate("LinkProjectV2ToTeam", query, variable)
-		if err != nil {
-			return err
-		}
-
-		if config.opts.exporter != nil {
-			return config.opts.exporter.Write(config.io, query.LinkProjectV2ToTeam.Team)
-		}
-		return printResults(config, query.LinkProjectV2ToTeam.Team.URL)
+		return linkTeam(c, owner, config)
 	}
-	return fmt.Errorf("specify at least one repo or team")
+	return nil
+}
+
+func linkRepo(c *api.Client, owner *queries.Owner, config linkConfig) error {
+	repo, err := api.GitHubRepo(c, ghrepo.New(owner.Login, config.opts.repo))
+	if err != nil {
+		return err
+	}
+	config.opts.repoID = repo.ID
+
+	query, variable := linkRepoArgs(config)
+	err = config.client.Mutate("LinkProjectV2ToRepository", query, variable)
+	if err != nil {
+		return err
+	}
+
+	if config.opts.exporter != nil {
+		return config.opts.exporter.Write(config.io, query.LinkProjectV2ToRepository.Repository)
+	}
+	return printResults(config, query.LinkProjectV2ToRepository.Repository.URL)
+}
+
+func linkTeam(c *api.Client, owner *queries.Owner, config linkConfig) error {
+	team, err := api.OrganizationTeam(c, ghrepo.New(owner.Login, ""), config.opts.team)
+	if err != nil {
+		return err
+	}
+	config.opts.teamID = team.ID
+
+	query, variable := linkTeamArgs(config)
+	err = config.client.Mutate("LinkProjectV2ToTeam", query, variable)
+	if err != nil {
+		return err
+	}
+
+	if config.opts.exporter != nil {
+		return config.opts.exporter.Write(config.io, query.LinkProjectV2ToTeam.Team)
+	}
+	return printResults(config, query.LinkProjectV2ToTeam.Team.URL)
 }
 
 func linkRepoArgs(config linkConfig) (*linkProjectToRepoMutation, map[string]interface{}) {
diff --git a/pkg/cmd/project/link/link_test.go b/pkg/cmd/project/link/link_test.go
index c1c32cb79..11d55983e 100644
--- a/pkg/cmd/project/link/link_test.go
+++ b/pkg/cmd/project/link/link_test.go
@@ -31,13 +31,13 @@ func TestNewCmdLink(t *testing.T) {
 			name:        "specify-nothing",
 			cli:         "",
 			wantsErr:    true,
-			wantsErrMsg: "specify at least one repo or team",
+			wantsErrMsg: "specify either `--repo` or `--team`",
 		},
 		{
 			name:        "specify-repo-and-team",
 			cli:         "--repo my-repo --team my-team",
 			wantsErr:    true,
-			wantsErrMsg: "specify only one repo or team",
+			wantsErrMsg: "specify only one of `--repo` or `--team`",
 		},
 		{
 			name: "repo",
@@ -316,8 +316,8 @@ func TestRunLink_Team(t *testing.T) {
 	defer httpReg.Verify(t)
 
 	httpReg.Register(
-		httpmock.GraphQL(`query OrganizationTeamList\b`),
-		httpmock.StringResponse(`{"data":{"organization":{"teams":{"nodes": [{"id": "team-ID", "slug": "my-team"}]}}}}`),
+		httpmock.GraphQL(`query OrganizationTeam\b`),
+		httpmock.StringResponse(`{"data":{"organization":{"team":{"id": "team-ID"}}}}`),
 	)
 	httpClient := newTestClient(httpReg)
 
diff --git a/pkg/cmd/project/unlink/unlink.go b/pkg/cmd/project/unlink/unlink.go
index ffed68f61..a361b3843 100644
--- a/pkg/cmd/project/unlink/unlink.go
+++ b/pkg/cmd/project/unlink/unlink.go
@@ -80,9 +80,9 @@ func NewCmdUnlink(f *cmdutil.Factory, runF func(config unlinkConfig) error) *cob
 			}
 
 			if config.opts.repo != "" && config.opts.team != "" {
-				return fmt.Errorf("specify only one repo or team")
+				return fmt.Errorf("specify only one of `--repo` or `--team`")
 			} else if config.opts.repo == "" && config.opts.team == "" {
-				return fmt.Errorf("specify at least one repo or team")
+				return fmt.Errorf("specify either `--repo` or `--team`")
 			}
 
 			// allow testing of the command without actually running it
@@ -121,50 +121,49 @@ func runUnlink(config unlinkConfig) error {
 	c := api.NewClientFromHTTP(httpClient)
 
 	if config.opts.repo != "" {
-		repo, err := api.GitHubRepo(c, ghrepo.New(owner.Login, config.opts.repo))
-		if err != nil {
-			return err
-		}
-		config.opts.repoID = repo.ID
-
-		query, variable := unlinkRepoArgs(config)
-		err = config.client.Mutate("UnlinkProjectV2FromRepository", query, variable)
-		if err != nil {
-			return err
-		}
-
-		if config.opts.exporter != nil {
-			return config.opts.exporter.Write(config.io, query.UnlinkProjectV2FromRepository.Repository)
-		}
-		return printResults(config, query.UnlinkProjectV2FromRepository.Repository.URL)
-
+		return unlinkRepo(c, owner, config)
 	} else if config.opts.team != "" {
-		teams, err := api.OrganizationTeams(c, ghrepo.New(owner.Login, ""))
-		if err != nil {
-			return err
-		}
-		for _, team := range teams {
-			if team.Slug == config.opts.team {
-				config.opts.teamID = team.ID
-				break
-			}
-		}
-		if config.opts.teamID == "" {
-			return fmt.Errorf("can't find team %s", config.opts.team)
-		}
-
-		query, variable := unlinkTeamArgs(config)
-		err = config.client.Mutate("UnlinkProjectV2FromTeam", query, variable)
-		if err != nil {
-			return err
-		}
-
-		if config.opts.exporter != nil {
-			return config.opts.exporter.Write(config.io, query.UnlinkProjectV2FromTeam.Team)
-		}
-		return printResults(config, query.UnlinkProjectV2FromTeam.Team.URL)
+		return unlinkTeam(c, owner, config)
 	}
-	return fmt.Errorf("specify at least one repo or team")
+	return nil
+}
+
+func unlinkRepo(c *api.Client, owner *queries.Owner, config unlinkConfig) error {
+	repo, err := api.GitHubRepo(c, ghrepo.New(owner.Login, config.opts.repo))
+	if err != nil {
+		return err
+	}
+	config.opts.repoID = repo.ID
+
+	query, variable := unlinkRepoArgs(config)
+	err = config.client.Mutate("UnlinkProjectV2FromRepository", query, variable)
+	if err != nil {
+		return err
+	}
+
+	if config.opts.exporter != nil {
+		return config.opts.exporter.Write(config.io, query.UnlinkProjectV2FromRepository.Repository)
+	}
+	return printResults(config, query.UnlinkProjectV2FromRepository.Repository.URL)
+}
+
+func unlinkTeam(c *api.Client, owner *queries.Owner, config unlinkConfig) error {
+	team, err := api.OrganizationTeam(c, ghrepo.New(owner.Login, ""), config.opts.team)
+	if err != nil {
+		return err
+	}
+	config.opts.teamID = team.ID
+
+	query, variable := unlinkTeamArgs(config)
+	err = config.client.Mutate("UnlinkProjectV2FromTeam", query, variable)
+	if err != nil {
+		return err
+	}
+
+	if config.opts.exporter != nil {
+		return config.opts.exporter.Write(config.io, query.UnlinkProjectV2FromTeam.Team)
+	}
+	return printResults(config, query.UnlinkProjectV2FromTeam.Team.URL)
 }
 
 func unlinkRepoArgs(config unlinkConfig) (*unlinkProjectFromRepoMutation, map[string]interface{}) {
diff --git a/pkg/cmd/project/unlink/unlink_test.go b/pkg/cmd/project/unlink/unlink_test.go
index 9e341cd8a..410322402 100644
--- a/pkg/cmd/project/unlink/unlink_test.go
+++ b/pkg/cmd/project/unlink/unlink_test.go
@@ -31,13 +31,13 @@ func TestNewCmdUnlink(t *testing.T) {
 			name:        "specify-nothing",
 			cli:         "",
 			wantsErr:    true,
-			wantsErrMsg: "specify at least one repo or team",
+			wantsErrMsg: "specify either `--repo` or `--team`",
 		},
 		{
 			name:        "specify-repo-and-team",
 			cli:         "--repo my-repo --team my-team",
 			wantsErr:    true,
-			wantsErrMsg: "specify only one repo or team",
+			wantsErrMsg: "specify only one of `--repo` or `--team`",
 		},
 		{
 			name: "repo",
@@ -316,8 +316,8 @@ func TestRunUnlink_Team(t *testing.T) {
 	defer httpReg.Verify(t)
 
 	httpReg.Register(
-		httpmock.GraphQL(`query OrganizationTeamList\b`),
-		httpmock.StringResponse(`{"data":{"organization":{"teams":{"nodes": [{"id": "team-ID", "slug": "my-team"}]}}}}`),
+		httpmock.GraphQL(`query OrganizationTeam\b`),
+		httpmock.StringResponse(`{"data":{"organization":{"team":{"id": "team-ID"}}}}`),
 	)
 	httpClient := newTestClient(httpReg)