FLAUM, Circuit Judge.
Jack D. Brocksmith owned several agencies in Quincy, Illinois, that specialized in selling insurance and annuities to the elderly. Unfortunately for his customers, Brocksmith began playing a shell game with their accounts. Brocksmith would receive premium payments from individuals who wanted to purchase insurance policies. He would delay submitting their insurance applications for six to eight weeks, in the meantime drawing on their money to pay for his personal expenses. If the customers complained that they were not receiving their policies, Brocksmith would say there was a problem with the insurance company; to handle things on that end, he would omit the date on the applications he forwarded, or white-out the real date and replace it with a later one. Eventually, when premiums from other customers came in, he would send their money to the carriers to cover the earlier applications, and repeat the cycle again.
In late 1986, Brocksmith sold several large policies or annuities issued by Fidelity Bankers Life Insurance Company. To Mary and Paul Sill, he sold two $25,000 single-premium deferred annuities. The $50,000 in premium checks were deposited into the general operating account of Brocksmith’s business. Brocksmith used the money to pay for all the insurance policies he had delayed up to that point and to pay his office expenses. That left only $18,000 remaining in the account.
In November of 1986, Brocksmith sold Jean and Irvin Klingler each a $50,000 single-premium life insurance policy. The Klinglers gave Brocksmith a $30,000 check up front, made out to his business rather than the insurance company. That way, Brocksmith explained, they would receive their interest immediately. In fact, Fidelity’s application form contained a tear-off receipt for the purchaser stating that the premium check should be made out to Fidelity, not the agent, and that Fidelity would decide within sixty days whether to issue the policy. This receipt was already torn off before the application reached the Klinglers. On December 1, Brocksmith sent a letter to the Klinglers indicating that he was forwarding their medical examination forms. He encouraged the Klinglers to take their time completing them, which they were forced to do anyway since Brock-smith did not actually mail the forms until four weeks later.
On December 4, Brocksmith sold Willade-an and Carl Sattman each a $50,000 single-premium life insurance policy. They gave Brocksmith a check for $25,000 as a down payment. He used this money to cover the Sills’ annuities. Later in the month, the Sattmans sent in the rest of their premium payment. At the beginning of January 1987, the Klinglers mailed a check for the $70,000 balance they owed. Brocksmith used these funds to pay for the Sattmans’ policies. Now all of his customers were accounted for, except the Klinglers, whose account (after all of Broeksmith’s machinations) was $78,000 short of the amount needed to complete their applications.
On February 6, the Klinglers mailed in their medical forms. Jean Klingler became worried because she had not received their policies. She tried several times, unsuccessfully, to reach Brocksmith on the phone. Eventually, on March 23, Brock-smith sent a postcard announcing that he would visit the Klinglers during April. When that date arrived, he sent a letter stating that due to an illness in his family he could not meet them until May. After a few more attempts to set up a meeting, Brocksmith sent another postcard to confirm a date of May 25.
During this time, Brocksmith was engaged in a last-ditch effort to avoid disaster. He conceived a plan to fake a robbery of his office — or, more precisely, of the Klinglers’ premium checks. Brocksmith told William Ratcliff, a former employee and current brother-in-law of his, that a large sum of money was missing from his account and was causing trouble between him and his wife. Brocksmith offered to pay Ratcliff if he would leave town and write a letter to his sister saying that he had taken the money. Ratcliff agreed. Brocksmith drove him to the train station in Burlington, Iowa, and bought him a ticket; from there, Ratcliff sent the deceitful letter to Mrs. Brocksmith.
Accompanied by his attorney, Brock-smith sat down with the Klinglers in late May to tell them the sad news that someone had broken into his office and stolen their premium checks. He confessed that he had endorsed the checks and left them in his office, and, showing them Ratcliff’s letter, speculated that his former employee was the thief. He tried to comfort the Klinglers with an offer to pay back $10,000 at once and $1000 a month thereafter. To show his good faith, he handed the Klin-glers a check for $10,000. Incredulous at his story, Jean Klingler refused to accept the offer. In the end, it would not have mattered if she had. The check bounced, and a replacement $10,000 money order sent via Federal Express had payment stopped on it a few days later.
Brocksmith called his insurance practice “rob[bing] Peter to pay Paul,” Tr. 130-31; a jury called it mail fraud. Brocksmith was convicted of five counts of violating 18 U.S.C. § 1341. Count 1 alleged that the Klinglers mailed a $70,000 check to Brock-smith; count 2 alleged that they mailed medical exam forms to him; count 3 alleged that Itatcliff mailed a letter to Brock-smith's wife; and counts 4 and 5 alleged that Brocksmith mailed two postcards to the Klinglers. Brocksmith was sentenced to three consecutive sentences of five years on counts 1 through 3, and suspended sentences on counts 4 and 5. He was also ordered to pay restitution to the Klinglers in the amount of $7100.
Brocksmith raises sixteen different arguments on appeal, some containing as many as eight subparts. He challenges the sufficiency of the evidence on all counts and the length of his sentence, objects to five witnesses' testimony, claims his trial attorney was ineffective and should have been disqualified, alleges prejudicial comments and ex parte communications by the district judge, and criticizes the jury instructions and voir dire questions. Many of these arguments were not made before the district court, are barely a page long in Brocksmith's oversized brief, and are wholly unsupported with case authority. Counsel bears responsibility for narrowing the issues presented on appeal from the entire universe of possible objections to the proceedings below to the small set of arguments that offer a legitimate chance for success. A client is disserved when the most meritorious arguments are drowned in a sea of words. "The premise of our adversarial system is that appellate courts do not sit as self-directed boards of legal inquiry and research, but essentially as arbiters of legal questions presented and argued by the parties before them." United States v. Berkowitz, 927 F.2d 1376, 1384 (7th Cir.) (quoting Carducci v. Regan, 714 F.2d 171, 177 (D.C.Cir.1983) (Scalia, J.)), cert. denied, - U.S. -, 112 S.Ct. 141, 116 L.Ed.2d 108 (1991). Undeveloped and unsupported claims are waived. See id.
Brocksmith's first argument is that his federal prosecution violated the Double Jeopardy Clause of the Fifth Amendment. Two years before this prosecution, the Assistant State's Attorney charged him with knowingly exerting unauthorized control over the Klinglers' assets. Brocksmith was found not guilty of this charge. He now contends that successive prosecutions for the same offense violate the Fifth Amendment. This argument, however, ignores the dual sovereignty doctrine, under which two sovereigns (such as the states and the federal government, see Heath v. Alabama, 474 U.S. 82, 89, 106 S.Ct. 433, 88 L.Ed.2d 387 (1985)) may prosecute an individual for the same conduct if it violates the laws of each. "The dual sovereignty doctrine has been a fixture of constitutional law for decades." United States v. Bafia, 949 F.2d 1465, 1478 (7th Cir.1991) (citing United States v. Lanza, 260 U.S. 377, 43 S.Ct. 141, 67 L.Ed. 314 (1922)), cert. denied, - U.S. -, 112 S.Ct. 1989, 118 L.Ed.2d 586 (1992).
Brocksmith contends that the district court should at least have held an eviden-tiary hearing to determine whether his federal prosecution was a "sham." The case of Bartkus v. Illinois, 359 U.S. 121, 79 S.Ct. 676, 3 L.Ed.2d 684 (1959), supposedly recognized an exception to the dual sovereignty doctrine in situations where one sovereign's prosecution serves as a tool for a second sovereign that previously prosecuted the defendant. See id. at 123-24, 79 S.Ct. at 678. We have questioned whether Bartkus truly meant to create such an exception, and we have uniformly rejected such claims. See United States v. Paiz, 905 F.2d 1014, 1024 (7th Cir.1990), cert. denied, - U.S. -, 111 S.Ct. 1319, 113 L.Ed.2d 252 (1991). In any event, conversations and cooperative efforts between state and federal investigators of the kind Brocksmith alleges are “undeniably legal” and are, in fact, “a welcome innovation” in law enforcement techniques. See id. at 1024 (quotation omitted).
Relatedly, Brocksmith argues that his federal prosecution was barred under the doctrine of collateral estoppel. The Double Jeopardy Clause has been held to embrace principles of issue preclusion, such that “when an issue of ultimate fact has once been determined by a valid and final judgment, that issue cannot again be litigated between the same parties in any future lawsuit.” Ashe v. Swenson, 397 U.S. 436, 443, 90 S.Ct. 1189, 1195, 25 L.Ed.2d 469 (1970); United States v. Bailin, 977 F.2d 270, 273-74 (7th Cir.1992). Collateral estoppel cannot apply here because it holds only between the same parties, whereas the United States was not represented in the prior case. See United States v. Sherman, 912 F.2d 907, 909 (7th Cir.1990).
Brocksmith’s next set of arguments challenge the sufficiency of the evidence used to prove him guilty of mail fraud. Brocksmith makes several claims that apply to one or another, or all, of the five counts: he argues (1) that the particular mailing occurred after the scheme to defraud had reached fruition; (2) that the particular mailing was not itself unlawful or fraudulent, and thus cannot form the basis of a mail fraud violation; and (3) that no pecuniary loss resulted from the mailing. Brocksmith can only succeed on these claims by demonstrating that no rational trier of fact could find the essential elements of the crime proved beyond a reasonable doubt. See United States v. Johnston, 876 F.2d 589, 593 (7th Cir.), cert. denied, 493 U.S. 953, 110 S.Ct. 364, 107 L.Ed.2d 350 (1989).
Brocksmith has, however, misconceived the elements of mail fraud. To establish a violation, the government must prove that a defendant “knowingly caused the mails to be used in furtherance of a scheme to defraud or to obtain money through false or fraudulent pretenses.” United States v. Kuzniar, 881 F.2d 466, 472 (7th Cir.1989). The use of the postal service need not be indispensable to the success of the scheme; a mailing may be merely “incident to an essential part of the scheme” or “a step in [the] plot.” Schmuck v. United States, 489 U.S. 705, 711, 109 S.Ct. 1443, 1448, 103 L.Ed.2d 734 (1989) (quotations omitted). The Schmuck Court held that an individual who purchased cars, turned back their odometers, and then sold them, committed mail fraud when the dealers sent the title-application forms to the state department of transportation. The Court distinguished the defendant’s ongoing fraud in Schmuck from other cases in which the pertinent mailings involved mere “accounting among the potential victims” of the scheme, occurring after the fraudulent scheme had reached fruition. Id. at 714, 109 S.Ct. at 1449. In Schmuck, by contrast, sending the registration forms to the transportation department was a key step in the successful passage of title — “a failure of this passage of title would have jeopardized Schmuck’s relationship of trust and goodwill with the retail dealers upon whose unwitting cooperation his scheme depended.” Id., 489 U.S. at 714-15, 109 S.Ct. at 1450.
Each of the mailings for which Brock-smith was indicted constituted a “step in the plot.” Receiving the $70,000 check was surely instrumental to Brocksmith’s scheme; indeed, it was his scheme. The mailing of the medical forms was also instrumental because it allowed Brocksmith to hold onto Klinglers’ money for a longer time; if the Klinglers failed to submit the forms, they would be entitled to a refund of their premiums. Paying Ratcliff to fabricate a story that he stole the Klinglers’ checks was plainly motivated by Brock-smith’s desire to buy time and, more importantly, an excuse for the missing money. Finally, the postcards were used to put the defendants at ease about the delays, as well as to gain more time for himself, and to conceal his misappropriation of the funds. Use of the mails to lull victims into a false sense of security, we have held, violates the mail fraud statute, even if it occurs after the money has been fraudulently obtained. United States v. Chappell, 698 F.2d 308, 311 (7th Cir.), cert. denied, 461 U.S. 931, 103 S.Ct. 2095, 77 L.Ed.2d 304 (1983). It does not matter that some of these mailings contained no false or misleading information, and individually caused no pecuniary loss; routine and innocent mailings can also supply an element of the offense of mail fraud. See Schmuck, 489 U.S. at 714-15, 109 S.Ct. at 1450 (citing Parr v. United States, 363 U.S. 370, 390, 80 S.Ct. 1171, 1183, 4 L.Ed.2d 1277 (1960)).
Brocksmith levels several charges against his appointed trial attorney, Ronald J. Stone. To begin with, Brocksmith alleges that Stone should have been disqualified due to a conflict of interest, because he occasionally acted as a Special Assistant Attorney General for the state of Illinois, representing state agencies in civil rights cases. Brocksmith says he wrote a letter to the clerk of the district court requesting that Stone be released, and a hearing on the matter was held before the district court, but all to no avail-the judge told Stone to continue representing him. Brocksmith neglects to mention one crucial fact in this story: he decided at the hearing to have Stone remain his lawyer. The district court advised Brocksmith that "[i]t would be very simple, very easy for the Court to relieve Mr. Stone of further providing representation to you and appoint another attorney to take over immediately and proceed ahead," Tr. 16, should Brock-smith so desire. Brocksmith responded that he was satisfied with Stone. Tr. 17. This argument is therefore waived. See United States v. Cirrincione, 780 F.2d 620, 624 (7th Cir.1985).
Brocksmith also accuses Stone, for the first time in this appeal, of rendering ineffective assistance of counsel. We have explained that ineffective assistance claims are better addressed at the district court level than on appeal, through a motion for new trial or collateral relief, due to the trial judge's superior opportunity to observe counsel's performance firsthand. See United States v. Limehouse, 950 F.2d 501, 503 (7th Cir.1991), cert. denied, - U.S. -, 112 S.Ct. 1962, 118 L.Ed.2d 563 (1992). In the interest of judicial efficiency, however, we will resolve an ineffective assistance claim "if the issue is sufficiently clear-cut." Johnson v. United States, 805 F.2d 1284, 1290 (7th Cir.1986). That is the case here. As discussed above, Brocksmith has waived any claim of conflict of interest on the part of his attorney. Brocksmith's other allegations are meritless. He complains that fifty-two out of the fifty-five exhibits offered by the government were irrelevant, and that his attorney should have objected to their introduction. Brock-smith cites no cases in support of his argument, nor elaborates on why the exhibits were irrelevant. Because he has shown neither cause nor prejudice under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), this argument fails.
The final challenges Brocksmith raises relate to his sentence. Brocksmith protests the district court's order that he pay restitution of $7100, claiming that the court did not consider the factors listed in 18 U.S.C. § 3580(a), such as the defendant's financial resources, needs, and earning ability. We have ruled that a sentence will be reversed when the defendant can show that it was "not improbable" that the judge failed to consider the requisite statutory factors and that the sentence was affected by this failure. See United States v. Studley, 892 F.2d 518 (7th Cir.1989). Brocksmith has made no such showing here. The one case he cites in support of reversal, United States v. Mahoney, 859 F.2d 47 (7th Cir.1988), involved a restitution order of $288,000 entered against a defendant who earned $30,000 a year. In those circumstances, we were persuaded that the district court had overlooked the defendant's financial capabilities when arriving at a dollar figure for restitution. An order to repay $7100, on the. other hand, does not invite the same inference.
Brocksmith also complains that three consecutive terms of 5 years yielded an excessive sentence. In this case, however, five separate violations of the mail fraud statute occurred. We have held that each mailing is a separate offense even if there is only one fraudulent scheme encompassing all the acts. See United States v. Ledesma, 632 F.2d 670, 679 (7th Cir.), cert. denied, 449 U.S. 998, 101 S.Ct. 539, 66 L.Ed.2d 296 (1980). The Sentencing Guidelines do not apply in this case because Brocksmith’s offenses occurred before November 1, 1987. See United States v. Stewart, 865 F.2d 115, 118 (7th Cir.1988). In the absence of the Guidelines’ mandatory penalty scheme, the district court retains great discretion to mete out punishments. 18 U.S.C. § 1341 authorizes a term of imprisonment of up to 5 years for each violation. Since Broeksmith’s sentence was within the statutory range, even if at the upper end, his total term of imprisonment was not improper.
Brocksmith’s conviction and sentence are Affirmed.
. For example, argument number fifteen states that 18 U.S.C. § 1341, the mail fraud statute, is unconstitutionally vague. It is disturbing enough that Brocksmith ignores the cases in which we have held expressly to the contrary. See, e.g., United States v. Suter, 755 F.2d 523, 527 n. 5 (7th Cir.), cert. denied, 471 U.S. 1103, 105 S.Ct. 2331, 85 L.Ed.2d 848 (1985); United States v. Feinberg, 535 F.2d 1004, 1010 (7th Cir.), cert. denied, 429 U.S. 929, 97 S.Ct. 337, 50 L.Ed.2d 300 (1976). But the real puzzle is why this argument does not appear until page 47 of Brocksmith's appellate brief, since it would moot all the other claims.
. The amount of restitution was only $7100 because Fidelity Bankers Life Insurance Company reached a settlement with the Klinglers whereby they received $92,900 in annuities. During her direct examination, Jean Klingler recalled the meeting when Brocksmith told her and her husband that their premium checks had been stolen. Jean Klingler testified that she told the defendant she could not accept his repayment offer because "it was our [life] savings. I was going to live on it for old age.” Tr. 182. Brock-smith did not object at the time, but argued later that he should be allowed to elicit on cross-examination the fact that the Klinglers obtained reimbursement from Fidelity. The district court refused to allow the question. We find no error. The amount of loss sustained by a victim is relevant and admissible evidence in a mail fraud prosecution. See United States v. Elliott, 771 F.2d 1046, 1051 (7th Cir.1985). The fact that a victim received partial reimbursement from another party is not ordinarily relevant. Even if the original testimony was prejudicial because it led the jury to believe, incorrectly, that the Klinglers never recovered their loss, counsel waived the argument by failing to object at the proper time. See United States v. Wynn, 845 F.2d 1439, 1442 (7th Cir.1988).