diff --git a/simapp/sim_test.go b/simapp/sim_test.go
index 5f9c3ca12eab..d99165a5fe5a 100644
--- a/simapp/sim_test.go
+++ b/simapp/sim_test.go
@@ -328,14 +328,23 @@ func TestAppStateDeterminism(t *testing.T) {
 
 	numSeeds := 3
 	numTimesToRunPerSeed := 5
-	appHashList := make([]json.RawMessage, numTimesToRunPerSeed)
 
+	// We will be overriding the random seed and just run a single simulation on the provided seed value
+	if config.Seed != simcli.DefaultSeedValue {
+		numSeeds = 1
+	}
+
+	appHashList := make([]json.RawMessage, numTimesToRunPerSeed)
 	appOptions := make(simtestutil.AppOptionsMap, 0)
 	appOptions[flags.FlagHome] = DefaultNodeHome
 	appOptions[server.FlagInvCheckPeriod] = simcli.FlagPeriodValue
 
 	for i := 0; i < numSeeds; i++ {
-		config.Seed = rand.Int63()
+		if config.Seed == simcli.DefaultSeedValue {
+			config.Seed = rand.Int63()
+		}
+
+		fmt.Println("config.Seed: ", config.Seed)
 
 		for j := 0; j < numTimesToRunPerSeed; j++ {
 			var logger log.Logger
diff --git a/x/group/simulation/genesis.go b/x/group/simulation/genesis.go
index 66b471fa5e47..7b533cf5daa3 100644
--- a/x/group/simulation/genesis.go
+++ b/x/group/simulation/genesis.go
@@ -66,21 +66,34 @@ func getGroupMembers(r *rand.Rand, accounts []simtypes.Account) []*group.GroupMe
 }
 
 func getGroupPolicies(r *rand.Rand, simState *module.SimulationState) []*group.GroupPolicyInfo {
-	groupPolicies := make([]*group.GroupPolicyInfo, 3)
+	var groupPolicies []*group.GroupPolicyInfo
+
+	usedAccs := make(map[string]bool)
 	for i := 0; i < 3; i++ {
 		acc, _ := simtypes.RandomAcc(r, simState.Accounts)
+
+		if usedAccs[acc.Address.String()] {
+			if len(usedAccs) != len(simState.Accounts) {
+				// Go again if the account is used and there are more to take from
+				i--
+			}
+
+			continue
+		}
+		usedAccs[acc.Address.String()] = true
+
 		any, err := codectypes.NewAnyWithValue(group.NewThresholdDecisionPolicy("10", time.Second, 0))
 		if err != nil {
 			panic(err)
 		}
-		groupPolicies[i] = &group.GroupPolicyInfo{
+		groupPolicies = append(groupPolicies, &group.GroupPolicyInfo{
 			GroupId:        uint64(i + 1),
 			Admin:          acc.Address.String(),
 			Address:        acc.Address.String(),
 			Version:        1,
 			DecisionPolicy: any,
 			Metadata:       simtypes.RandStringOfLength(r, 10),
-		}
+		})
 	}
 	return groupPolicies
 }
diff --git a/x/simulation/client/cli/flags.go b/x/simulation/client/cli/flags.go
index bec5b6e8b712..43f0e4c52465 100644
--- a/x/simulation/client/cli/flags.go
+++ b/x/simulation/client/cli/flags.go
@@ -6,6 +6,8 @@ import (
 	"github.com/cosmos/cosmos-sdk/types/simulation"
 )
 
+const DefaultSeedValue = 42
+
 // List of available flags for the simulator
 var (
 	FlagGenesisFileValue        string
@@ -39,7 +41,7 @@ func GetSimulatorFlags() {
 	flag.IntVar(&FlagExportParamsHeightValue, "ExportParamsHeight", 0, "height to which export the randomly generated params")
 	flag.StringVar(&FlagExportStatePathValue, "ExportStatePath", "", "custom file path to save the exported app state JSON")
 	flag.StringVar(&FlagExportStatsPathValue, "ExportStatsPath", "", "custom file path to save the exported simulation statistics JSON")
-	flag.Int64Var(&FlagSeedValue, "Seed", 42, "simulation random seed")
+	flag.Int64Var(&FlagSeedValue, "Seed", DefaultSeedValue, "simulation random seed")
 	flag.IntVar(&FlagInitialBlockHeightValue, "InitialBlockHeight", 1, "initial block to start the simulation")
 	flag.IntVar(&FlagNumBlocksValue, "NumBlocks", 500, "number of new blocks to simulate from the initial block height")
 	flag.IntVar(&FlagBlockSizeValue, "BlockSize", 200, "operations per block")